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1.
Alternate Exterior Angles Converse: If two lines are cut by a transversal so the alternate exterior angles are congruent, then the two lines are parallel.

2.
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

3.
Alternate Interior Angles Converse: If two lines are cut by a transversal so the alternate interior angles are congruent, then the two lines are parallel.

4.
Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

5.
Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

6.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of second triangle, then the two triangles are congruent.

7.
Base Angles Theorem: If two sides of a triangle are congruent, then the angles opposite them are congruent.

8.
Concurrency of Altitudes of a Triangle: The lines containing the altitudes of a triangle are concurrent.

9.
Concurrency of Angle Bisectors of a Triangle: The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.

10.
Concurrency of Medians of a Triangle: 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.

11.
Concurrency of Perpendicular Bisectors Theorem: The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.

12.
Congruent Complements Theorem: If two angles are complementary to the same angle (or to congruent angles), then the two angles are congruent.

13.
Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent.

14.
Consecutive Interior Angles Converse: If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the two lines are parallel.

15.
Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

16.
Converse of the 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.

17.
Converse of the Base Angles Theorem: If two angles of a triangle are congruent, then the sides opposite them are congruent.

18.
Converse of the Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.

19.
Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

20.
Converse of the Pythagorean Theorem: If the square of the length of the longest side of a traingle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle

21.
Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

22.
Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

23.
Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

24.
Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

25.
Lines Perpendicular to a Transversal Theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

26.
Midsegment Theorem: The segment connecting the midpoint of two sides of a triangle is parallel to the third side and is half as long as that side.

27.
Perpendicular Bisector Theorem: If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

28.
Perpendicular Transversal Theorem: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

29.
Properties of Angle Congruence: Angle congruence is reflexive, symmetric, and transitive.

30.
Properties of Segment Congruence: Segment congruence is reflexive, symmetric, and transitive.

31.
Properties of Triangle Congruence: Triangle congruence is reflexive, symmetric, and transitive.

32.
Pythagorean 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.

33.
Right Angles Congruence Theorem: All right angles are congruent.

34.
Side-Angle-Side (SAS) Similarity Theorem: If an angle of one triangle is congruent to an angle of a second triangle and the lengths or the sides including these angles are proportional, the the triangles are similar.

35.
Side-Side-Side (SSS) Similarity Theorem: If the corresponding side lengths of two triangles are proportional, the the triangles are similar.

36.
Third Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

37.
Transitive Property of Parallel Lines: If two lines are parallel to the same line, then they are parallel to each other.

38.
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

39.
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

40.
Triangle Sum Theorem: The sum of the measures of the interior angles of a triangle is 180.

41.
Vertical Angles Congruence Theorem: Vertical angles are congruent.

## Geometry 1-6 and 7.1 and 7.2 TheoremsStudy online at quizlet.com/_53q9k |

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