Lesson 4-3: Congruent Triangles TARGETS Name and use corresponding parts of congruent polygons. Targets

LESSON 4-3: Congruent Triangles Concept 1

LESSON 4-3: Congruent Triangles EXAMPLE 1 Identify Corresponding Congruent Parts Show that the polygons 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. Ex1: ID Corr Cong parts

Answer: x = 25.5, y = 9 Use Corresponding Parts of Congruent Triangles LESSON 4-3: Congruent Triangles Use Corresponding Parts of Congruent Triangles EXAMPLE 2 In the diagram, ΔITP  ΔNGO. Find the values of x and y. WORK REASONS O  P CPCTC mO = mP Def of congruence 6y – 14 = 40 Substitution 6y = 54 y = 9 CPCTC NG = IT Def of congruence x – 2y = 7.5 Substitution x – 2(9) = 7.5 x – 18 = 7.5 x = 25.5 Answer: x = 25.5, y = 9 Ex2: CPCTC

LESSON 4-3: Congruent Triangles Concept 2

Use the Third Angles Theorem LESSON 4-3: Congruent Triangles 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. WORK REASONS ∆JIK  ∆JIH Congruent Triangles Triangle Angle Sum Theorem mKJI + mIKJ + mJIK = 180 H  K, I  I, and J  J CPCTC 72 + 72 + mJIK = 180 Substitution 144 + mJIK = 180 mJIK = 36 mJIK = mJIH Third Angles Theorem 36 = mJIH Substitution Ex3: 3rd Ang Th

Use the Third Angles Theorem LESSON 4-3: Congruent Triangles EXAMPLE 3 Use the Third Angles Theorem TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ∆KLM  ∆NJL, KLM  KML and mKML = 47.5, find mLNJ. Ex3: Try on your own

Concept 3