Page 139 - Math Course 3 (Book 2)

Proportional Relationships of Similar Triangles

JK JL MO. 10 - L5b
Substitute in the equation to get
=
QR QS
JK
2JM
2JM
JK
. Simplify to find , Special Segments of Similar
=
=
QR 2QT QR 2QT Triangles
Therefore, △JKM ~△QRT by SSS Similarity.
Your Turn! THEOREMS
Special Segments of Similar Triangles
Perimeters of Similar Triangles
10.8 If two triangles are similar, then the mea-
If △PNO ~ △XQR, PN = 6, XQ = 20, QR = 20√2, sures of the corresponding altitudes are
and RX = 20, find the perimeter of △PNO. proportional to the measures of the
corresponding sides.
Q
Abbreviation: ~△s have corr. altitudes
proportional to the corr. sides.
U
N 20
Q
20√2
6
T W V
P O X 20 R
P A R
A. 18√2 QA PR QR PQ
= = =
B. 6√2 UW TV UV TU
C. 12 + 6√2
D. 72√2
10.9 If two triangles are similar, then the mea-
sures of the corresponding angle bisectors
Answer of the triangle are proportional to the mea-
sures of the corresponding sides.

Write a Proof Abbreviation: ~△s have corr. ∠bisectors
5 proportional to the corr. sides.
△EFG ~ △MSY and EF = MS. Find the ratio of
4
the length of a median of △EFG to the length of a U
median of △MSY. Q

A. 4
5 T X V

1 P B R
B.
4
QB PR QR PQ
= = =
1 UX TV UV TU
C.
5

D. 5
4

Answer

131