Page 110 - Math Course 3 (Book 2)

Comparing Similar Figures

The scale factor that relates MNOP to ABCD is
3 1 MONUMENTS
Use the scale factor to relate
or
12 4 Suppose the San Jacinto Monument
dimensions in MNOP, x, to dimensions in ABCD, y. in LaPorte, Texas, casts a shadow of
285 feet at the same time a nearby
tourist, who is 5 feet tall, casts a
y = kx Direct variation equation. 2.5-feet shadow. How tall is the San
Jacinto Monument?
1
d = (33) Substitute.
4 Explore
You know the lengths of the
d = 8.25 Multiply shadows and the height of the
tourist. You need to find the height
of the San Jacinto Monument.
Answer The value of x is 8.25.
Plan
Write and solve a proportion.

Real World Example Solve
tourist’s tourist’s
MAPS shadow → 2.5 5 ← height
=
A surveyor wants to find the distance RS across building’s → 285 h ← building’s
the lake. He constructs ΔPQT similar to ΔPRS and shadow height
measures the distances as shown. What is the
distance across the lake? 2.5 • h = 285 • 5 Find the cross products.

2.5h = 1425 Multiply.
h = 570 Divide each side by 2.5.

The height of the San Jacinto
Answer
Monument is 570 feet.

The scale factor that relates ΔPQT to ΔPRS is
25 5 Your Turn!
60 or 12 Find Measures of Similar Figures

y = kx Direct variation equation. The figures are similar. Find the missing measure.

5
12 = x Substitution. M 5 m N
12
3m
144 = 5x Multiply each side by 12. O P
R 10 m S
144
= x Divide each side by 5.
5 x m

28.8 = x U T
A. 1.5 m B. 6 m
C. 10 m D. 16.7 m
The distance across the lake
Answer
is 28.8 meters. Answer

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