Page 140 - Math Course 3 (Book 2)

Proportional Relationships of Similar Triangles

10.10 If two triangles are similar, then the mea-
sures of the corresponding medians are Let’s Begin
proportional to the measures of the
corresponding sides.

Abbreviation: ~△s have corr. Medians of Similar Triangles
medians proportional to the corr. sides.

U Example
Q

In figure, △EFD ~ △JKI. EG is a median of △EFG,
T Y V and JL is median of △JKL. Find JL if EF = 36,
ED = 18, and JK = 56.
P M R
J
QM PR QR PQ
= = =
UY TV UV TU

E I
THEOREM 7.11 L K

Angle Bisector Theorem
An angle bisector in a triangle separates to oppo- D G F
site side into segments that have the same ratio as EG EF
the other two sides. = Write a proportion.
JL JK
Example: AD = AC ← segments with vertex A 18 36 EG = 18, JL = x, EF = 36,
DB BC ← segments with vertex B x = 56 and JK = 56

C 1008 = 36x Cross products.

28 = x Divide each side by 36.

Answer Thus, JL = 28.
A D B

Solve Problems with Similar Triangles

Example

The drawing below illustrates two poles supported △ABC ~ △GED and BF and EC are medians of
by wires. △ABC ~ △GED, AF ≅ CF, and FG ≅ GC ≅ △ABC ~ △GED since AF ≅ CF and GC ≅ DC. If two
DC. Find the height of the pole EC.
triangles are similar, then the measure of the
B
corresponding medians are proportional to the
E
measures of the corresponding sides. This leads
30
AC
BF
ft to the proportion .
=
A F G C D EC GD
80 ft Since AF = CF, CF measure 40 ft. Also, since FG = GC =
40 ft DC, GC and DC both measure 20 ft. Therefore, GD = 40.
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