1. Concept 1

2. Example 1 Identify Corresponding Congruent Parts Show that polygons ABCDE and RTPSQ are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ. Sides: Angles:

3. A.A B.B C.C D.D Example 1 The support beams on the fence form congruent triangles. In the figure ΔABC  ΔDEF, which of the following congruence statements directly matches corresponding angles or sides? A. B. C. D.

4. Example 2 Use Corresponding Parts of Congruent Triangles  O  PCPCTC m  O=m  PDefinition of congruence 6y – 14=40Substitution In the diagram, ΔITP  ΔNGO. Find the values of x and y.

5. Example 2 Use Corresponding Parts of Congruent Triangles 6y=54Add 14 to each side. y=9Divide each side by 6. NG=ITDefinition of congruence x – 2y=7.5Substitution x – 2(9)=7.5y = 9 x – 18=7.5Simplify. x=25.5Add 18 to each side. CPCTC Answer: x = 25.5, y = 9

6. A.A B.B C.C D.D Example 2 A.x = 4.5, y = 2.75 B.x = 2.75, y = 4.5 C.x = 1.8, y = 19 D.x = 4.5, y = 5.5 In the diagram, ΔFHJ  ΔHFG. Find the values of x and y.

7. Concept 2 You will prove this!

8. Example 3 Use the Third Angles Theorem ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If  J   K and m  J = 72, find m  JIH. GIVEN: ΔJIK  ΔJIH

9. Example 3 Use the Third Angles Theorem Answer: m  JIH = 36

10. A.A B.B C.C D.D Example 3 A.85 B.45 C.47.5 D.95 TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM  ΔNJL,  KLM   KML and m  KML = 47.5, find m  LNJ.

11. Example 4 Prove That Two Triangles are Congruent Write a two-column proof. Prove:ΔLMN  ΔPON

12. Example 4 Prove That Two Triangles are Congruent Proof: StatementsReasons

13. Example 4 Find the missing information in the following proof. Prove:ΔQNP  ΔOPN Proof: ReasonsStatements  Q   O,  NPQ   PNO 1. 1. Given

14. Concept 3