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

2. LESSON 4-3: Congruent Triangles
Concept 1

3. 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

4. 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 = Substitution
6y = 54
y = 9
CPCTC
NG = IT Def of congruence
x – 2y = Substitution
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
Answer: x = 25.5, y = 9
Ex2: CPCTC

5. LESSON 4-3: Congruent Triangles
Concept 2

6. 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
mJIK = Substitution
144 + mJIK = 180
mJIK = 36
mJIK = mJIH Third Angles Theorem
36 = mJIH Substitution
Ex3: 3rd Ang Th

7. 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

8. Concept 3