A. A

B. B

C. C

D. D

Find the distance between the points. Express answers in simplest radical form and as decimal approximations rounded to the nearest hundredth, if necessary.

(over Lesson 10-5)

10(9,2) and (3,10)

(–2, –4) and (3, 8)13

(–5, 0) and (1, –7)

–36 or 12

Find the possible values of a if (9, –12) and (2, a) are 25 units apart.

• similar triangles

• Determine whether two triangles are similar.

• Find the unknown measures of sides of two similar triangles.

Animation: Similar Triangles

Determine whether the pair of triangles is similar. Justify your answer.

Determine Whether Two Triangles Are Similar

Determine Whether Two Triangles Are Similar

Answer: The corresponding sides of the triangles are proportional, so the triangles are similar.

1. A

2. B

3. C

0%0%0%

A B C

A. The triangles are similar.

B. The triangles are not similar.

C. cannot be determined

Determine whether the pair of triangles is similar.

Find Missing Measures

A. Find the missing measures if the pair of triangles is similar.

Corresponding sides of similar triangles are proportional.

Find Missing Measures

CE = 8, GI = y, ED = 18, and GH = 27

216 = 18y Find the cross products.

12 = y Divide each side by 18.

Corresponding sides of similar triangles are proportional.

CD = 18, GH = 27, ED = 18, and IH = x

18x = 486 Find the cross products.

x = 27 Divide each side by 18.

Answer: The missing measures are 27 and 12.

Find Missing Measures

Corresponding sides of similar triangles are proportional.

XY = 4, XZ = 10, XW = 3, and XV = a.

4a= 30 Find the cross products.

B. Find the missing measure if the pair of triangles is similar.

Find Missing Measures

a = 7.5 Divide each side by 4.

Answer: The missing measure is 7.5.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 14 and 28

B. 6 and 42

C. 18 and 28

D. 18 and 42

A. Find the missing measures if the pair of triangles is similar.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 5.25

B. 6

C. 16

D. 14

B. Find the missing measure if

SHADOWS Richard is standing next to the General Sherman 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 2 meters, how tall is the tree?

Since the length of the shadow of the tree and Richard’s height are given in meters, convert the length of Richard’s shadow to meters.

1 m = 100 cm

= 0.536 m Simplify.

Let x = the height of the tree.

Answer: The tree is about 84 meters tall.

Richard’s shadow

Tree’s shadow

Richard’s height

Tree’s height

0.536x = 45 Cross products

x ≈ 83.96

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 2 m

B. 0.98 m

C. 3.2 m

D. 1.45 m

TOURISM Trudie is standing next to the Eiffel Tower in France. The height of the Eiffel Tower is 317 meters and casts a shadow of 155 meters. If Trudie’s height is 2 meters, how long is her shadow?

Chapter 10 Lesson 6 homework:

Worksheet page 46