Basic Mathematics for College Students

Chapter 9 Summary and Review 823

Property of similar triangles
If two triangles are similar, all pairs of
corresponding sides are in proportion.

LANDSCAPING A tree casts a shadow 27 feet long at the same time

as a man 5 feet tall casts a shadow 3 feet long. Find the height of the

tree.

If we let the height of the tree, we can find by solving the

following proportion.

The height of the tree The length of the tree’s shadow

The height of the man  The length of the man’s shadow

 

Similar triangles are h h

determined by the

tree and its shadow

and the man and his

shadow. Since the

triangles are similar,

the lengths of their

corresponding sides

3 ft 27 ft are in proportion.

5 ft

h

Find each cross product and set them equal.

Do the multiplication.

To isolate h,divide both sides by 1.3.

Do the division.

The tree is 45 feet tall.

h 45

3 h

3



135

3

3 h 135

3 h5(27)

h

5



27

3

52.

53.

54.

Determine whether the triangles are similar.

55. 
    
    
    
    56. 
        
    
    
    
    


56. In the figure below,. Find and.


57. HEIGHT OF A TREE A tree casts a 26-foot
    shadow at the same time a woman 5 feet tall casts
    a 2-foot shadow. What is the height of the tree?
    (Hint:Draw a diagram first and label the side
    lengths of the similar triangles.)

32 7

8

16

T

S

M

x

R N

y

O

RSTMNO x y

35°

35°

50°

50°

50°

50°

50° 60°

6 cm

50° 60°

6 cm

60° 50°

70° 70°

60° 50°

70° 70°

REVIEW EXERCISES

Determine whether the triangles in each pair are congruent. If
they are, tell why.

51. 3 in. 3 in.

3 in.

3 in. 3 in.

3 in.

BY

Z

X

A

C

32°

61°

6 in.

9 in.

49. Two congruent triangles are shown below. Complete
    the list of corresponding parts.
    a. corresponds to.
    b. corresponds to.
    c. corresponds to.
    d. corresponds to.
    e. corresponds to.
    f. corresponds to.


50. Refer to the figure below, where.

a. Find.

b. Find.

c. Find.

d. Find .m(AC)

m(YZ)

m(C)

m(X)

ABC  XYZ

A B

CF

E D

BC

AB

AC

C^

B^

A^