Question

A geologist wants to determine the distance across the widest part of a nearby lake. The geologist marked off specific points around the lake so that the line containing segment DE would be parallel to the line containing BC. The segment BC is selected specifically because it is the widest part of the lake. The segment DE is selected specifically because it is a short enough distance to easily measure. Use this diagram to answer the following questions.

1. Is ADE similar to ABC'? How do you know? *

Yes. All three sides are proportional.
Yes. Two or more angles are equivalent.
No. Side lengths are not proportional.
There is insufficient information to determine similarity.

2. If ADE is similar to ABC, and |AD| = 1,200 ft and |AB| = 3,600 ft, what is the length of segment BC?

2,700 ft
1,600 ft
2,100 ft
2,400 ft

3. If ABC is similar to ADE what is the length of segment AC? *
5 points
2,000 ft
3,000 ft
2,400 ft
2,800 ft

Answer 1

1. Yes. Two or more angles are equivalent

2. 2700 ft

3. 3000 ft

Explanation:

1.

∠EAD = ∠CAB (same angle)

∠AED = ∠ACB (because AC is a straight line and ED and CB are parallel)

2.

1200:3600

1:3

This means that for any given side for triangle AED, the corresponding side for triangle ACB is three times bigger. ED corresponds to CB, so:

900 x 3 = 2700

3.

We know that for any given side for triangle AED, the corresponding side for triangle ACB is three times bigger. AE corresponds to AC, so:

1000 x 3 = 3000