Table of Contents Date: 10/19 Topic: Congruent Triangles Description: Making congruency statements using corresponding parts of congruent triangles. Page: 17

Chapter 4 Section 3

Congruent Polygons Congruence Statement Question, Topics and Vocabulary Problems, Definitions and Work   Congruent Polygons Two polygons are _____________ if and only if their _______________________ ___________________. Congruence Statement List corresponding vertices in the _______________________. Valid statement using triangles above:

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 is congruent to ∆DEF, which of the following congruence statements correctly identifies corresponding angles or sides? MULTIPLE CHOICE a) Angle ABC is congruent to angle EFD   b) Angle BAC is congruent to angle DFE c) Side BC is congruent to side DE d) Side AC is congruent to side DF

CPCTC If two polygons are _____________, then their   CPCTC If two polygons are _____________, then their ______________________________________ _________________________________. We say:

Example 2: a) In the diagram, ∆ITP congruent to ∆NGO. Find the values of x and y.

Example 2: b) In the diagram, ∆FHJ is congruent to ∆HFG. Find the values of x and y.

BRAIN BREAK! http://ellentube.com/videos/0-xkw1n2gp/

Third Angles Theorem If two angles of one triangle are _______________   Third Angles Theorem If two angles of one triangle are _______________ to two angles of a second triangle, then the ________________ of both triangles are _________________.

Example 3: ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If Angle IJK is congruent to angle IKJ and measure of angle IJK = 72, find measure of angle JIH.

Reflexive Property of Triangle Congruence   Reflexive Property of Triangle Congruence Symmetric Property of Triangle Congruence Transitive Property of Triangle Congruence

Summary! 1. In the diagram, ∆LMN ≅ ∆RST. Find the values of x and y.

Summary! 2. If triangle FGH is congruent to triangle JKI, name the corresponding angles.

Summary! 3. If ∆RPG is congruent to ∆FAS. Name all of the congruent corresponding sides and corresponding angles.  

Summary! 4. Complete the congruence statement ∆VUT ≅ ___________________.