Lessons

1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

Proving Congruent Triangles

Objective:

•    Prove two triangles are congruent by using the SSS postulate, the SAS Postulate, the ASA Postulate, AAS theorem, and HL Theorem.

Lesson 4-2 Proving Congruent Triangles

 Postulate 12 (SSS Postulate) If three sides of one triangles are congruent to three sides of another triangle, then the triangles are congruent. Triangle ABC is congruent to Triangle DEF by SSS Postulate   Postulate 13 (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.   Triangle ABC is Congruent to Triangle DEF by SAS Postulate   Postulate 14 (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 triangle are congruent.   Triangle ABC is Congruent to Triangle DEF by ASA Postulate   Theorem 4-1 (The Isosceles Triangle Theorem) If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Angle A is Congruent to Angle C by the Isosceles Triangle Theorem Corollary 1 An equilateral triangle is also equiangular Corollary 2 An equilateral triangle has three 60 degree angles Corollary 3 The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint   Theorem 4-2 If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollary An equiangular triangle is also equilateral   Theorem 4-3 (AAS Theorem) If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Triangle ABC is congruent with triangle DEF by the AAS theorem   Theorem 4-4 (HL Theorem) If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. Triangle ABC is Congruent with triangle DEF by the HL Theorem Note: This theorem only applies to right triangles. The side opposite from the right triangle is called the hypotenuse. The other two sides are called legs.

Quickie Math Copyright (c) 2000 Team C006354