Page 138 - Math Course 3 (Book 2)

Proportional Relationships of Similar Triangles
Mo. 10

Lesson 5 Proportional
XY = perimeter of△XYZ Perimeter
AB perimeter of △ABC Theorem

KEY CONCEPTS: 24 = x Substitution.
16 48 + 16√5
1. Recognize and use proportional
relationships of corresponding 24 (48 + 16√5) = 16x Cross products.
perimeters of similar triangles.
2. Recognize and use proportional 1152 + 384√5 = 16x Multiply.
relationships of corresponding angle Divide each
bisectors, altitudes, and medians of 72 + 24√5 = x side by 16.
similar triangles.
The perimeter of
Answer
MO. 10 - L5a △XYZ is 72 + 24√5 units.

Proportional Perimeters of

Similar Triangles Write a Proof

THEOREM 10.7 Example

Proportional Perimeters Theorem Write a paragraph proof.
If two triangles are similar, then the perimeters are
proportional to the measures of corresponding Given: △JKL ~ △QRS
sides. MK is a median of △JKL.
TR is a median of △QRS.
Prove: △JKM ~ △QRT
Let’s Begin J

Perimeters of Similar Triangles
E I K
Example L

D F
If △ABC ~ △XYZ, AC = 32, AB = 16, BC = 16√5, G
and XY = 24, find the perimeter of △XYZ.

Answer
B 16√5 Proof:
JK JL
=
Y By definition of similar triangles .
QR
QS
16
Since similar triangles corresponding medians
JL KM
proportional to the corresponding sides
=
A 32 C QS RT
JK
24 By substitution Since MK and TR are
LM
=
QR RT
medians of △JKL and △QRS, respectively, M and T
X Z
are midpoints of JL and QS. By definition of
Let x represent the perimeter of △XYZ. The perimeter midpoint, 2JM=JL and 2QT = QS.
of △ABC = 16 + 16 or 48 + 16 5
5 + 32
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