Properties of Triangles and Heights

The video tutorial explains how to find the height of an equilateral triangle using the properties of a 30-60-90 triangle. It begins by introducing the concept of an equilateral triangle and drawing its height, which divides the triangle into two 30-60-90 triangles. The tutorial then explains the properties of a 30-60-90 triangle, where the short leg is x, the hypotenuse is 2x, and the long leg is x√3. Using these properties, the video demonstrates how to calculate the height of the triangle with different side lengths, providing a step-by-step example with a side length of 8.

What is the measure of each angle in an equilateral triangle?

• 60°

• 45°

• 90°

• 120°

When an altitude is drawn in an equilateral triangle, what type of triangles are formed?

• Two 60-60-60 triangles

• Two 30-60-90 triangles

• Two 90-90-90 triangles

• Two 45-45-90 triangles

In a 30-60-90 triangle, if the short leg is X, what is the length of the hypotenuse?

• X/2

• 2X

• X√3

• X

If the side of an equilateral triangle is 3, what is the height?

• 9

• 6

• 3√3

• 3

What happens to the base of an equilateral triangle when an altitude is drawn?

• It remains the same

• It doubles

• It is divided into two equal parts

• It becomes zero

If each side of an equilateral triangle is 8, what is the height?

• 4√3

• 8

• 4

• 8√3

In a 30-60-90 triangle, what is the relationship between the short leg and the long leg?

• The long leg is the same as the short leg

• The long leg is twice the short leg

• The long leg is the short leg times √3

• The long leg is half the short leg

What is the formula for the height of an equilateral triangle in terms of its side length X?

• X√3

• X√3/2

• 2X

• X/2