Page 106 - Math Course 3 (Book 2)

Similar Triangles

Find Missing Measures
Find the missing measures if the pair of triangles

Examples is similar. △XYW ~ △XZV

Find the missing measures if the pair of triangles
is similar. Z
10 cm

C 18 Y

770
4 cm
8 260 D
X V
770
3 cm W
E 18
a cm
G 27

770
XY XW Corresponding sides of similar
y 260 H =
XZ XV triangles are proportional.
770
4 3 XY = 4, XZ = 10, XW = 3,
I x =
10 a and XV = a.
Since the corresponding angle have equal
measures, △CDE ~ △GHI. The lengths of the 4a = 30 Find the cross products.
corresponding sides are proportional.

CE CD Corresponding sides of similar a = 7.5 Divide each side by 4.
GI = GH triangles are proportional.

8 18 CE = 8, GI = y, ED = 18, and
y = 27 GH = 27 Answer The missing measure is 7.5.

216 = 18y Find the cross products.
Real World Example
12 = y Divide each side by 18.
SHADOWS
CD = ED Corresponding sides of similar Richard is standing next to the General Sherman
GH IH triangles are proportional. Giant Sequoia tree in Sequoia National Park. The
shadow of the tree is 22.5 meters, and Richard’s
shadow is 53.6 centimeters. If Richard’s height is
18 = 18 CD = 18, GH = 27, ED = 18, and 2 meters, how tall is the tree?
27 x IH = x.

18x = 486 Find the cross products.

x = 27 Divide each side by 18. 2 m x m

53.6 cm 25.5 cm
The missing measures are 27 Since the length of the shadow of the tree and
Answer Richard’s height are given in meters, convert the
and 12.
length of Richard’s shadow to meters.

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