Identify Corresponding Congruent Parts Show that polygons ABCDE

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. Angles: Sides: Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ.

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. A B C D

Use Corresponding Parts of Congruent Triangles In the diagram, ΔITP ΔNGO. Find the values of x and y. O P CPCTC m O = m P Definition of congruence 6 y – 14 = 40 Substitution

Use Corresponding Parts of Congruent Triangles 6 y = 54 Add 14 to each side. y = 9 Divide each side by 6. CPCTC NG = IT Definition of congruence x – 2 y = 7. 5 Substitution x – 2(9) = 7. 5 x – 18 = 7. 5 Simplify. x 25. 5 Add 18 to each side. = Answer: x = 25. 5, y = 9 y=9

In the diagram, ΔFHJ ΔHFG. Find the values of x and y. 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 A. B. C. D. A B C D

You will prove this!

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

Use the Third Angles Theorem Answer: m JIH = 36

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. A. 85 B. 45 C. 47. 5 D. 95 A. B. C. D. A B C D

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

Prove That Two Triangles are Congruent Proof: Statements Reasons

Find the missing information in the following proof. Prove: ΔQNP ΔOPN Proof: Statements 1. Q O, NPQ PNO Reasons 1. Given