# Lesson 3

Half an Equilateral Triangle

- Let’s investigate the properties of altitudes of equilateral triangles.

### Problem 1

Select **all** statements that are true about equilateral triangle \(ABC\).

Angles \(B\) and \(C\) are 60 degrees.

\(x = 3\sqrt{3}\)

\(x = 6\sqrt{3}\)

Triangle \(ABD\) is congruent to triangle \(ACD\).

\(BD\) 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.

### Problem 5

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

3 units

\(\frac{3}{\sqrt2}\) units

\(3 \sqrt2\) units

6 units

### 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?

The angle would decrease.

The angle would remain the same.

The angle would increase.

We cannot determine anything about the angle.

### Problem 7

Segment \(A’B’\) is parallel to segment \(AB\).

- What is the length of segment \(A'B'\)?
- What is the length of segment \(B’B\)?

### Problem 8

Here is triangle \(POG\). Match the description of the rotation with the image of \(POG\) under that rotation.