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Theorems from Chapters 2-6

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Question
Answer
All right angles are congruent   Right Angles Congruence Theorem  
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The sum of the lengths of any two sides of a triangle is greater than the length of the third side   Triangle Inequality Theorem  
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If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths   Perimeters of Similar Polygons Theorem  
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Vertical Angles are congruent   Vertical Angles Congruence Theorem  
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If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent   Alternate Interior Angles Congruent  
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If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent   Alternate Exterior Angles Congruent  
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If two parallel lines are cut by a transversal, then the consecutive interior (co-interior) angles are supplementary   Consecutive Interior (Co-Interior) Angles Supplementary  
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If two lines are cut by a transversal and alternate interior angles are congruent, then the two lines are parallel   Alternate Interior Angles Converse  
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If two lines are cut by a transversal and alternate exterior angles are congruent, then the two lines are parallel   Alternate Exterior Angles Converse  
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If two lines are cut by a transversal and co-interior angles are supplementary, then the two lines are parallel   Co-Interior Angles Converse  
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If two lines are parallel to the same line, then they are parallel to each other   Transitive for Parallel Lines  
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The sum of the measures of the interior angles of a triangle is 180 degrees   Triangle Sum Theorem  
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles   Exterior Angle Theorem  
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If the corresponding side lengths of two triangles are proportional, then the triangles are similar   Side-Side-Side Similarity (SSS Sim)  
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If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar   Side-Angle-Side Similarity (SAS Sim)  
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If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent   Angle-Angle-Side (AAS) Congruence Theorem  
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If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent   Angle-Side-Angle (ASA) Congruence Theorem  
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If two sides of a triangle are congruent, then the angles opposite the sides are congruent   Base Angles Theorem  
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If a triangle is equilateral, then the triangle is equiangular   Corollary to the Base Angles Theorem  
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If two angles of a triangle are congruent, then the sides opposite the angles are congruent   Base Angles Converse  
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If a triangle is equiangular, then the triangle is equilateral   Corollary to the Base Angles Converse  
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The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side   Midsegment Theorem  
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If a point is on a perpendicular bisector of a segment, then it is on the perpendicular bisector of the segment   Perpendicular Bisector Theorem  
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If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.   Converse of the Perpendicular Bisector Theorem  
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The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle   Circumcenter Theorem  
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If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle   Angle Bisector Theorem  
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If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle   Converse of the Angle Bisector Theorem  
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The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle   Incenter Theorem  
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The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side   Centroid Theorem  
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