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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 

Definition
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 

