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| The sum of the measures of the angles of a triangle is 180. |
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| an extra line or segment drawn in a figure to help analyze geometric relationships |
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| angles formed by one side of a triangle and the extension of an adjacent side |
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| the 2 angles not adjacent to the exterior angle; each exterior angle has 2 |
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| The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles |
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| uses statements written in boxes and arrows to show the logical progression of the argument |
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| theorem with a proof that follows as a direct result of another theorem |
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| the acute angles of a right triangle are complementary |
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| there can be at most one right or obtuse angle in a triangle |
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| two geometric figures that are exactly the same size and shape. |
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| 2 polygons in which all the parts of one polygon are congruent to the corresponding parts or matching parts of the other |
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| parts of two geometric figures that are congruent |
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| definition of congruent polygons |
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| two polygons are congruent if and only if their corresponding parts are congruent |
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| if two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent |
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| properties of triangle congruence |
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Reflexive:
▲ABC≅▲ABC
Symmetric:
If ▲ABC≅▲EFG, then ▲EFG≅▲ABC.
Transitive:
If ▲ABC≅▲EFG and ▲EFG≅JKL, then ▲ABC≅▲JKL. |
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| if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. |
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| the angle made by two adjacent lines is the included angle of those lines |
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| if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. |
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| the side located between two consecutive angles of a polygon |
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| if two angles and a third side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. |
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| if two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent. |
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4.6
legs of an isosceles triangle |
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| two congruent sides of an isosceles triangle |
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| the angle formed by the legs of an isosceles triangle |
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| two angles formed by the base and the two congruent sides of an isosceles triangle |
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| isosceles triangle theorem |
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| if two sides of a triangle are congruent, then the angles opposite those sides are congruent |
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| converse of isosceles triangle theorem |
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| if two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
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| a triangle is equilateral if and only if it is equiangular |
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| each angle of an equilateral triangle measures 60 |
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| operation that remaps an original geometric figure |
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| the original geometric figure in a transformation |
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| new geometric figure in a transformation |
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| congruence transformation |
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| one in which the image may differ from that of the preimage, but the two figures remain congruent. |
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| see congruence transformation |
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| a flip over a line called the line of reflection. each point of the preimage and image are the same distance from the line of reflection. |
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| a slide that moves all points of the original figure the same distance in the same direction |
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| rurn around a fixed point called the center of rotation, through a specific angle, and in a specific direction. Each point in the preimage and image are the same distance from the center of rotation. |
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| use figures in the coordinate plane and algebra to prove geometric concepts |
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