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Thm Chap 2-7

Theorems from Chapters 2-7

All right angles are congruent Right Angles Congruence Theorem
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle Pythagorean Acute Triangle Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side Triangle Inequality Theorem
Vertical Angles are congruent Vertical Angles Congruence Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent Alternate Interior Angles Congruent
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Alternate Exterior Angles Congruent
If two parallel lines are cut by a transversal, then the consecutive interior (co-interior) angles are supplementary Consecutive Interior (Co-Interior) Angles Supplementary
If two lines are cut by a transversal and alternate interior angles are congruent, then the two lines are parallel Alternate Interior Angles Converse
If two lines are cut by a transversal and alternate exterior angles are congruent, then the two lines are parallel Alternate Exterior Angles Converse
If two lines are cut by a transversal and co-interior angles are supplementary, then the two lines are parallel Co-Interior Angles Converse
If two lines are parallel to the same line, then they are parallel to each other Transitive for Parallel Lines
The sum of the measures of the interior angles of a triangle is 180 degrees Triangle Sum Theorem
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
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs Pythagorean Theorem
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle Converse of Pythagorean Theorem
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
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
If two sides of a triangle are congruent, then the angles opposite the sides are congruent Base Angles Theorem
If a triangle is equilateral, then the triangle is equiangular Corollary to the Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite the angles are congruent Base Angles Converse
If a triangle is equiangular, then the triangle is equilateral Corollary to the Base Angles Converse
If the corresponding side lengths of two triangles are proportional, then the triangles are similar Side-Side-Side Similarity (SSS Sim)
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)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent Hypotenuse-Leg (HL) Congruence
If the square of the length of the longest side of a triangle is greater than the of the squares of the lengths of the other two sides, then the triangle is obtuse. Pythagorean Obtuse Triangle Theorem
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
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
If a point is on a perpendicular bisector of a segment, then it is on the perpendicular bisector of the segment Perpendicular Bisector Theorem
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
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle Circumcenter Theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle Angle Bisector Theorem
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
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle Incenter Theorem
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 Cenroid Theorem
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original and to each other Similar Right Triangles Theorem
Created by: warnockj