A Survey of Mathematics with Applications (11th Edition)

Chapter 8

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Parallel ; Any two lines in the same plane are ... more

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skew ; Skew lines are the lines that do not lie in... more

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Angle ; An angle is denoted by the symbol .The ... more

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Complementary ;  If the sum of the measure of two ... more

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Supplementary ; If the sum of the measure of two ... more

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Straight ; Angles are classified based on their ... more

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Right ; Angles are classified based on their ... more

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Obtuse ; Angles are classified based on their ... more

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Acute ; Angles are classified based on their ... more

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Vertical  ;  When two straight lines intersect, ... more

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; Draw a figure representing the rays and . ; ... more

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; Draw a figure representing the half lines   and... more

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; Draw a figure representing the half open line ... more

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; Draw a figure representing a half line and a ... more

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; Draw a figure representing the half lines   and... more

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; Draw a figure representing , , and . ; The ... more

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; Draw a figure representing the half open line ... more

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; Draw a figure representing a half line and a ... more

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; Draw a figure representing and . ; From the ... more

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; Draw a figure representing and . ;  The ... more

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; Draw a figure representing the half line and ... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two complementary angles is .... more

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; The sum of any two supplementary angles is .... more

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; The sum of any two supplementary angles is .... more

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; The measure of any two vertical angles is same.... more

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; The measure of any two vertical angles is same.... more

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; The measure of any two vertical angles is same... more

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; The sum of any two supplementary angles is . In... more

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; The sum of any two complementary angles is .  ... more

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; ; The sum of any two complementary angles is .... more

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;  The sum of any two complementary angles is .  ... more

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; The sum of any two complementary angles is .... more

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; The sum of any two supplementary angles is . ... more

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; The sum of any two supplementary angles is .   ... more

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; The sum of any two supplementary angles is .... more

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, ; Any two planes that do not intersect each ... more

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, ; A plane is said to be at right angle to the ... more

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, , ; From the figure, the plane and intersects ... more

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, , ; From the figure, the intersection of planes... more

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, ; The plane has the lines , and points , , and... more

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, ; The plane has the lines , , and .The line ... more

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Always true: If is parallel to and is parallel ... more

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Sometimes true: In an equilateral triangle, all ... more

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Sometimes true: The statement is true only if the ... more

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Sometimes true. The statement is true only if the ... more

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Sometimes true: The statement is true only if the ... more

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Never true: If two angles of a triangle are obtuse... more

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Line ; Draw a sketch representing two distinct ... more

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Infinite ;  Draw a sketch of a line and draw the ... more

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No, the statement is not true. It is possible that... more

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No, the statement is not true. It is possible that... more

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; Sketch a figure such that two different lines ... more

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The following definition is made by the ... more

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Following are the three classic geometry problems ... more

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The basic constructions that can be made using a ... more

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Polygon ; A closed figure start and end at the ... more

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Regular ; A regular polygon has all the sides ... more

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Proportion ; Figures that have same shape but may ... more

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; The sum of the measures of the interior angles ... more

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Congruent ; Equal length of corresponding sides in... more

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; The sum of the measures of the interior angles ... more

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Square ;  In the given figure, both pairs of the ... more

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Rectangle ;  In the given figure, both the pairs ... more

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Trapezoid ; In the given figure, one pair of ... more

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Parallelogram ;  In the given figure, both pairs ... more

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Rhombus ; In the given figure, the opposite sides ... more

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Trapezoid ; In the given figure, only two pairs of... more

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; In the given figure, and are supplementary ... more

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; The sum of supplementary angles is equal to .In... more

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; The sum of supplementary angles is equal to .In... more

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; In the given figure, and are vertical angles ... more

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; In the given figure, and are alternate ... more

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; Alternate interior angles are equal.In the ... more

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; If a polygon has sides, then the sum of its ... more

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; If a polygon has sides, then the sum of its ... more

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; If a polygon has sides, then the sum of its ... more

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; If a polygon has sides, then the sum of its ... more

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; If a polygon has sides, then the sum of its ... more

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2016 ; As the given figures are similar to each ... more

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3016 ; As the given figures are similar to each ... more

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610 ; As the given figures are similar to each ... more

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8 ; As the given figures are similar to each other... more

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20 ; As the given figures are similar to each ... more

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1620 ; As the given figures are similar to each ... more

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3 ; Let length of side be .As the given figures ... more

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; Let length of side be .As the given figures ... more

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; Let length of side be .As the given figures ... more

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2 ; Let length of side be .As the given figures ... more

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33 ; Triangle is congruent to triangle .... more

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34 ; Triangle is congruent to triangle .... more

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18 ; Triangle is congruent to triangle .... more

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; Triangle is congruent to triangle .... more

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; Triangle is congruent to triangle .... more

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; Triangle is congruent to triangle .... more

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9 ; Quadrilateral is congruent to quadrilateral .... more

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11 ; Quadrilateral is congruent to quadrilateral... more

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10 ; Quadrilateral is congruent to quadrilateral... more

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; Quadrilateral is congruent to quadrilateral .... more

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; Quadrilateral is congruent to quadrilateral .... more

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70 ft ; The triangle formed by the shadow of silo ... more

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; As is isosceles, so, .Substitute for and ... more

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;  From the given figure, it can be seen that ... more

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; From the given figure, it can be seen that and... more

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Surveyor Leonard Digges, who was a British ... more

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Most of the geometrical shapes, such as lines, ... more

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Hypotenuse ; The hypotenuse is the sum of the ... more

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Circle ; A circle is a two dimensional figure ... more

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; Substitute 7 for and 5 for into the formula ... more

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; Convert the base of a given figure into cm ... more

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; Convert the height of a given triangle into ... more

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; The side of the square is equal to the diameter... more

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; The radius of a semicircle is half its diameter... more

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; Let the side of the inner square be .The ... more

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; The length and width of the vertical rectangle ... more

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; Substitute 9 for , 11 for , and 18 for into ... more

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; Substitute 4 for into the formula for the area... more

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; Since the diameter of the circle is 10 m, ... more

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; The radius of the bigger circle is 12 mm.Divide... more

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; In the given figure, a rectangle of length 24 ... more

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; Substitute for into the given expression and ... more

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; Substitute for into the given expression and ... more

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; Multiply the number of in the given expression... more

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; Divide the number of in the given expression ... more

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; Area of a rectangle is given by , where is the... more

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; Area of a rectangle is given by , where is the... more

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; Area of a rectangle is given by , where is the... more

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; Area of a rectangle is given by , where is the... more

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; The area of a rectangle is given by, where is ... more

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; The area of a rectangle is given by , where is... more

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21 feet ; The ladder, the side wall, and the ... more

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40 feet ; The rope, the dock, and the sea level ... more

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312 feet ; Let the distance between the home plate... more

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in. ;  The angles in a rectangle are right angles... more

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;  Calculate by using the formula .Substitute 6 ... more

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Basketball court: ; ; Take the official dimension ... more

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The given statement does not satisfy the property ... more

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James Garfield proved the Pythagorean theorem by ... more

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The ancient Babylonians use 3 as the value of and ... more

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Volume ; A three dimensional figure has volume and... more

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Surface ; A three dimensional figure is made up of... more

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Platonic ; Polyhedron is a closed figure which is ... more

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Prism ; A polyhedron that have congruent polygon ... more

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Right ; Prism is a type of polyhedron where the ... more

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2 ; For a polyhedron, the polygonal regions ... more

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2400 ; The given three-dimensional figure is a ... more

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720 ; The given three-dimensional figure is a ... more

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; The given 3-dimensional figure is a pyramid ... more

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; Let the volume of a complete cuboid be , where... more

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; The given 3-dimensional figure is a cone.Use ... more

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; The given 3-dimensional figure of the complete ... more

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; The given 3-dimensional figure of complete ... more

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; The given 3-dimensional figure is a trapezoidal... more

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; The given 3-dimensional figure is a cylinder.... more

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; The given 3-dimensional figure is a cuboid.Find... more

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; The given 3- dimensional figure of the complete... more

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; Apply the relation .Multiply by 27 to convert ... more

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; Since , divide both sides by 27 to obtain the ... more

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; Since , divide both sides by 27 to obtain the ... more

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13,700,000 ; Apply the relation .Multiply by 1,... more

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; Since , divide both sides by 1,000,000 to ... more

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; Since , divide both sides by 1,000,000 to ... more

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;  From the given figure, the upper case is a ... more

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Tub :; Box: ; Since the shape of tubs are right ... more

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; The diameter of the cone is 6 inches, find the ... more

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; Find the radius of the cylinder by dividing ... more

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8 times ; Assume the side of the cube to be Find ... more

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8 times ; Assume the radius of the sphere to be .... more

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Initial Cost of air conditioner in the room with ... more

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Pappus of Alexandria’s best-known work is Synagoge... more

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Reflection ; Reflection is a motion in which a ... more

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Translation ; Translation is a motion wherea ... more

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Vector ;  A translation includes both magnitude ... more

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Rotation ; A rotation is a motion in which a ... more

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Rotation ; The angle at which a figure is rotated ... more

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Glide ; A glide reflection is a motion in which ... more

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Symmetry ;  A geometric figure is said to be ... more

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Tessellation ; Tessellation or tilling is a ... more

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Reflect the vertices ,  ,  , and   about the line... more

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Connect the points ,  ,  , and . ; more

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Reflect the vertices ,  , and   about the line .... more

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Reflect the vertices , , and about the line .The ... more

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Reflect the vertices , , , and about the line .... more

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Reflect the vertices , , , and about the line .... more

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 Reflect the centre about the line .The ... more

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Reflect the centre about the line .The ... more

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Shift the vertices, , and by 5 units to the right... more

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Translate the vertices, , and 2 units to the left ... more

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Translate the vertices, , , and 2 units to the ... more

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Translate the vertices, , , and 5 units to the ... more

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Translate the vertices, , , , and 5 units to the ... more

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Translate the vertices , , , , and 2 units to the... more

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Translate the vertices , , , , , , , and 2 units ... more

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Translate the vertices , , , , , , , and 5 units ... more

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Rotate the vertices , , , and in counter-... more

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Rotate the vertices , , , and in counter-... more

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Rotate the vertices , , and in counter-clockwise... more

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Rotate the vertices , , and in counter-clockwise... more

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Rotate the vertices , , , and in counter-... more

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Rotate the vertices , , , and in counter-... more

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Rotate the vertices , , , and in counter-... more

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Rotate the vertices , , , and in counter-... more

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Shift the vertices , , and 4 units to the right ... more

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Shift the vertices , , and 3 units up along the ... more

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Shift the vertices , , , and 4 units down along ... more

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Shift the vertices , , , and 3 units to the left ... more

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Shift the vertices , , , and 3 units to the right... more

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Shift the vertices , , , and 3 units up along the... more

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Shift the vertices , , , and 2 units down along ... more

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Shift the vertices , , , and 3 units to the right... more

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Letters B, C, D, E, H, I, K, O, X ; Draw the ... more

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Letters A, H, I, M, O, T, U, V, W, X, Y ; Draw the... more

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Letters H, I, N, O, S, X, Z ; Rotate the capital ... more

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Symmetry plays an important role in biology to get... more

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M.C. Escher exploited the basic patterns by using ... more

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Rubber ; Topology is the branch of mathematics ... more

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;  On drawing a line on the surface of the strip... more

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Klein ; The bottle, which is formed by stretching ... more

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Four ; Bythe “Four Color” theory, any map sketched... more

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Jordan ; In topology,a geometrical figure similar ... more

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Genus ; The maximum numberof holes that can be ... more

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; By “Four Colour” theory, any map sketched in a ... more

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;  By “Four Colour” theory, any map sketched in ... more

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; By “Four Colour” theory, any map sketched in ... more

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;   By “Four Colour” theory, any map sketched in ... more

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;  Any map sketched in plane surface can be drawn... more

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; Any map sketched in plane surface can be drawn ... more

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;  Any map sketched in plane surface can be drawn... more

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; Any map sketched in plane surface can be drawn ... more

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Outside ; To find whether the point is outside or ... more

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Inside ; To find whether the point is outside or ... more

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Inside ; To find whether the point is outside or ... more

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Outside ; To find whether the point is outside or ... more

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0 ;  Genus represents the maximum number of holes ... more

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1 ; Genus represents the maximum number of holes ... more

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5 ;  Genus represents the maximum number of holes ... more

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5 ; Genus represents the maximum number of holes ... more

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1 ; Genus represents the maximum number of holes ... more

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3 ; Genus represents the maximum number of holes ... more

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2 ; Genus represents the maximum number of holes ... more

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Larger than 5 ; Genus represents the maximum ... more

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Larger than 5 ; Genus represents the maximum ... more

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4 ;  Genus represents the maximum number of holes ... more

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0 ; Genus represents the maximum number of holes ... more

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1 ; In the experiment, a strip is formed using a ... more

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1 ;  In the experiment, a strip is formed using a... more

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1 ; In the experiment, a strip is formed using a ... more

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Two ; In the experiment, a strip is formed using ... more

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The smaller strip is Mobius and the longer strip ... more

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Yes ;  By twisting one whole and a half times, the... more

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     ; As the number of genus present in both ... more

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; According to the "Four Colour" theorem, any map... more

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The result in both the experiments will be same ... more

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; According to the "Four Colour" theorem, any map... more

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Mobius strip is a continuous loop with only one ... more

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Parallel ; By fifth axiom of Euclidean geometry, ... more

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no ; According to the fifth axiom of elliptical ... more

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two ; The fifth axiom of hyperbolic geometry ... more

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plane ; Euclidean geometry is the study of flat ... more

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Sphere ; The elliptical geometry is a non-... more

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Pseudosphere ; The hyperbolic geometry is a non-... more

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Geodesic ; In non-Euclidean geometry, a geodesic ... more

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Chaos ; Chaos theory is a branch of mathematics ... more

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; Make a fractal-like diagram, start with the ... more

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; Make a fractal-like diagram, start with the ... more

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; Make a fractal-like diagram, start with the ... more

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; Make a fractal-like diagram, start with the ... more

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Each geometry is used within its parameters or its... more

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Spherical – Elliptical geometryFlat – Euclidean ... more

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Coastlines, tree, mountains, rivers, galaxies, and... more

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               ; An angle is the union of two rays... more

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; An angle is the union of two rays with a common... more

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;  A triangle is the union of three rays with ... more

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; A half line segment is the part of a line ... more

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; A line segment is the part of a line between ... more

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; It is known that a half line is the part of a ... more

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; The sum of complimentary angles is .Let the ... more

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; The sum of two supplementary angles is .Let the... more

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in. ; Let the length of be .As the triangles ... more

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inch ; Let the length of be . As the triangles ... more

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; As triangles and are similar, the lengths of ... more

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; As triangles and are similar, the lengths of ... more

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; The value of is as vertically opposite angles... more

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; The formula to calculate the sum of measures of... more

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square meter ;  The diameter of each circle is 10... more

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;  The given figure is in a square shape from ... more

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; Apply the formula of area of rectangle,, withas... more

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; Let the base of the prism be a triangle. ... more

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28 cubic feet ; Let be the height of the triangle... more

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; Apply the formula, , as is the radius of the ... more

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        ; Apply the formula for the volume of the ... more

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; Let the reflection of triangle  be .Vertex   is... more

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; Let the reflection of triangle be .Vertex is ... more

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; Let the translation of rectangle be rectangle... more

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; Let the translation of rectangle be rectangle... more

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; Since is positive, the trapezoid is to be ... more

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; Since is positive, the trapezoid is to be ... more

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; Since is positive, the trapezoid is to be ... more

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 Let be the triangle obtained after the required ... more

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 Let be the triangle obtained after the required ... more

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Yes; Because the reflected triangle has beginning... more

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No; Because the reflected triangle does not have ... more

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No; Because the rotated rectangle does not have ... more

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Yes; Because the rotated rectangle has beginning ... more

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; Let four colors be orange, green, purple, and ... more

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Outside ;  A Jordan curve is a topological object,... more

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If a line is given and a point, which is not on ... more

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; Draw a square.Replace each side of the square ... more

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; Draw an equilateral triangle. ; Replace each ... more

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; It is known that an angle is the union of two ... more

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; It is known that a triangle is the union of ... more

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;  It is known that a point is the union of two ... more

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; The union of ray and is that part of line , ... more

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; The sum of complimentary angles is .Let the ... more

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; The sum of two supplementary angles is .Let the... more

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; One angle of the triangle is , as vertically ... more

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; Apply the formula to calculate the sum of the ... more

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cm ; Let be the length of .Two figures are similar... more

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; Substitute 6 for , 4 for , and 3 for into the ... more

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112 cubic feet ; Substitute 4 for and 7 for into... more

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; Let the reflection of rectangle   be .Vertex   ... more

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; Let the translation of quadrilateral be ... more

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; Since is positive, the triangle is to be ... more

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 Let the translation of rectangle be rectangle . ... more

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A Möbius strip is a surface, which has 1 side and ... more

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