6th Grade Math Textbook, Progress

Use Proportions

11-8

10 ft

6 ft

O h

M N

h

20 ft

R

P Q

MNO

PQR

6

h




1

2

0

0

6  20  10 h

120  10  10 h 10

12 h

The tree is 12 ft tall.

Apply the Division Property of Equality.

Use the cross-products rule.

Write a proportion.

Proportions in similar triangles can be useful

for indirect measurement, such as finding

heights of objects that are too large to be

measured directly.

To solve shadow problems, you can draw

a pair of similar right triangles.

A 6-ft-tall person is standing near a tree. If the

person’s shadow is 10 ft long and the tree’s

shadow is 20 ft long, what is the height of the tree?

To find the height of the tree, h, draw a pair of similar right triangles.

Then write and solve a proportion.

light ray

light ray

shadow cast by

taller structure

shadow cast by

shorter structure

taller

structure shorter

structure

10 yd

45 yd

60 yd

 ^45

MN

10

60

MA

MN

DA

NE

Study this example.

Gil found the distance across a pond, MN, by

measuring land distances and setting up

similar triangles as shown in the given figures.

What is the distance across the pond?

Write a proportion.

10 MN 60  45

10 MN 10  2700  10

MN 270

The distance across the pond is 270 yards.

Use the cross-products rule.

Apply the Division Property of Equality.

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