__Geometry Chapter 4 Study Guide__

1) ** The Angle Sum Theorem:** The sum of the measures of the angles of a triangle is 180.

2) ** Third Angle Theorem:** If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

3) ** The Exterior Angle Theorem:** The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

4) ** Corollary:** The acute angles of a right triangle are complementary.

5) ** Corollary:** There can be at most one right or one obtuse angle in a triangle.

6) Congruence of triangles is reflexive, symmetric, and transitive.

7) ** SSS Postulate: **If the sides of one triangle are one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

8) ** SAS Postulate: **If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

9) ** ASA Postulate:** If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

10) ** AAS Theorem:** If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and the nonincluded side of second triangle, then the triangles are congruent.

11) ** The Isosceles Triangle Theorem:** If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

12) ** The Converse of the Isosceles Triangle Theorem:** If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

13) ** Corollary:** A triangle is equilateral if and only if it is equiangular.

14) ** Corollary:** Each angle in an equilateral triangle measures 60°.

__Important vocabulary:__

1) acute triangle

2) auxiliary line

3) base (of an isosceles triangle)

4) base angles (of an isosceles triangle)

5) congruent triangles

6) corollary

7) equiangular triangle

8) equilateral triangle

9) exterior angle (of a triangle)

10) included angle

11) included side

12) isosceles triangle

13) legs (of an isosceles triangle)

14) obtuse triangle

15) remote interior angles

16) right triangle

17) scalene triangle

18) triangle

19) vertex angle

*You test may ask for the following:*

1) Define any 10 of the 19 terms above.

2) Prove any 2 statements above.

Or… something else.

**For additional proof practice: Pg231 #42-45 and Pg210-211 #25-31**

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