Indirect Measurement

Warm-UpSolve each proportion.

1. 3 X 2. 6 2.45 75 X 8

3. 9 X 4. X 8 27 6 3.5 7

= =

= =

X = 45 X = 20

X = 2 X = 4

What we are doing…

Learn to find measures indirectly by applying the properties of similar figures.

Indirect Measurement….

F

E G

A

B C

Notice how all angles are congruent.

A

B C

A

B

C

A

B

C

A

B

A

B

C

Notice what happens as we turn the triangle.

Which angle corresponds with angle E?

Which angle corresponds with angle F?

BA

Example 1;

Triangles ABC and EFG are similar. Find the length of side EG.

B

A C

3 ft

4 ft

F

E G

9 ft

X

Triangles ABC and EFG are similar.

1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river?

Question 1:

The diagram:

W

7 m

21 m

15 mWork…

Question 2:

Julie wants to know how far it is from her house to the big oak tree. She drew a diagram and labeled it with her known measurements. How far is the tree from her house?

Diagram….

5 ft

6 ft 4 ft

24 ft16 ft

Work…..

Question 3

A yardstick casts a 2-ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree?

??

6 ft

3 ft

2 ft

Question 4;

A 30 ft building casts a shadow that is 18 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree?

30 ft

18 ft 3 ft

?????

Question 5

Triangles with triangles…

AC = 30DC = 20

BE = 4

AB = ?

E

B

D

C A

Question 6;

E

B

D

C A

AC = 24DC = ?

BE = 8

AB = 4