Transcript File

Lesson 4-3: Congruent Triangles
TARGETS
• Name and use corresponding parts of
congruent polygons.
LESSON 4-3: Congruent Triangles
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.
LESSON 4-3: Congruent Triangles
EXAMPLE 2 Use Corresponding Parts of Congruent
Triangles
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
x – 2y = 7.5
Def of congruence
Substitution
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
Answer: x = 25.5, y = 9
LESSON 4-3: Congruent Triangles
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
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.