4.3 Congruent Triangles Then: You identified and used congruent angles. Now: 1. Name and use corresponding parts of congruent triangles. 2. Prove triangles.

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4.3 Congruent Triangles Then: You identified and used congruent angles. Now: 1. Name and use corresponding parts of congruent triangles. 2. Prove triangles congruent using the definition of congruence.

4.3 Congruent Triangles Corresponding parts-  BCA   EFD Corresponding angles: Corresponding sides:

Example 1: a. Identify all pairs of congruent corresponding parts. Write another congruence statement for the triangles.  JKL   NKM Corresponding angles:  ___   ___

Example 1 cont. Corresponding Sides: _____  _____ Congruence statement:  ______   ______

Example 1: Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. b. c. _________________ ______________

Example 2: In the diagram,  ABC   DEF a. Find the value of x. b. Find the value of y.

Example 2: In the diagram, Δ FHJ  Δ HFG. c. Find the value of x. d. Find the value of y.

Theorem 4.3-Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent.

Example 3: a. TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If Δ KLM  Δ NJL,  KLM   KML, and m  KML = 47.5, find m  LNJ.

Example 3: Find the value of y. b. c.

Example 4: Prove that triangles are congruent. a. Given: FH  JH, FG  JG,  FHG   JHG,  FGH   JGH Prove:  FGH   JGH Statements Reasons 1. FH  JH, FG  JG1. _________________ 2. HG  HG2. _________________ 3.  FHG   JHG,3. _________________  FGH   JGH 4.  HFG   HJG4. __________________ 5.  FGH   JGH5. __________________

Theorem 4.4- Properties of Triangle Congruence Reflexive Property of Triangle Congruence:  ABC   ABC. Symmetric Property of Triangle Congruence : If  ABC   DEF, then  DEF   ABC. Transitive Property of Triangle Congruence : If  ABC   DEF and  DEF   JKL, then  ABC   JKL.

Example 4: b. In the diagram, E is the midpoint of AC and BD. Show that  ABE   CDE.

4.2 Assignment: p #10,11, 13-16, 18-20, 23, 24, 28, 30, 34, 35, 37, 43-46, 48-50, #23 and 24 proofs on handout