Warm Up

4.3 Congruent Triangles Unit 2 Chapter 4

Congruent Figures If two geometric figures have exactly the same shape and size, they are congruent.

Congruent Polygons In two congruent polygons, all of the parts of one polygon are congruent to the corresponding parts or matching parts of the other polygon. These corresponding parts include corresponding angles and corresponding sides.

Definition of Congruent Polygons

Congruent Statements Other congruence statements for the triangles above exist. Valid congruence statements for congruent polygons list corresponding vertices in the same order.

Example 1 a) Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.

Example 1 b) The support beams on the fence form congruent triangles. In the figure ∆ABC  ∆DEF, which of the following congruence statements correctly identifies corresponding angles or sides?

“If and Only If” The phrase “if and only if” in the congruent polygon definition means that both the conditional and converse are true. So, if two polygons are congruent, then their corresponding parts are congruent. For triangles we say Corresponding Parts of Congruent Triangles are Congruent or CPCTC.

Example 2 a) In the diagram, ∆ITP  ∆NGO. Find the values of x and y.

Example 2 b) In the diagram, ∆FHJ  ∆HFG. Find the values of x and y.

Third Angles Theorem

Example 3 ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If  IJK   IKJ and m  IJK = 72, find m  JIH.

Example 4

StatementsReasons 1.1. Given 2.  LNM   PNO Third Angles Theorem 4. ΔLMN  ΔPON 4

Properties of Triangle Congruence