# Lesson 3

Half an Equilateral Triangle

### Problem 1

Select all statements that are true about equilateral triangle $$ABC$$.

A:

Angles $$B$$ and $$C$$ are 60 degrees.

B:

$$x = 3\sqrt{3}$$

C:

$$x = 6\sqrt{3}$$

D:

Triangle $$ABD$$ is congruent to triangle $$ACD$$.

E:

$$BD$$ and $$CD$$ are both 3 units long.

### Problem 2

Find the length of each leg.

### Problem 3

An equilateral triangle has a side length of 10 units. What is its area?

### Problem 4

Find the lengths of the legs.

### Solution

(From Unit 4, Lesson 2.)

### Problem 5

A square has side length 3 units. What is the length of the diagonal?

A:

3 units

B:

$$\frac{3}{\sqrt2}$$ units

C:

$$3 \sqrt2$$ units

D:

6 units

### Solution

(From Unit 4, Lesson 2.)

### Problem 6

A step has a height of 5 inches. A ramp starts 4 feet away from the base of the step, making a $$5.9^\circ$$ angle with the ground. What can you say about the angle the ramp would make with the ground if the ramp starts farther away from the step?

A:

The angle would decrease.

B:

The angle would remain the same.

C:

The angle would increase.

D:

We cannot determine anything about the angle.

### Solution

(From Unit 4, Lesson 1.)

### Problem 7

Segment $$A’B’$$ is parallel to segment $$AB$$.

1. What is the length of segment $$A'B'$$?
2. What is the length of segment $$B’B$$?

### Solution

Here is triangle $$POG$$. Match the description of the rotation with the image of $$POG$$ under that rotation.