Properties of Triangles and Squares

The video tutorial covers solving geometry problems involving equilateral triangles and squares. It begins with setting up and solving a problem to find the perimeter of an equilateral triangle using its altitude. Next, it addresses finding the perimeter of a square given its diagonal. Finally, it explains how to determine the altitude of an equilateral triangle when the perimeter is known.

What is the first step in solving the word problems discussed in the video?

• Draw a picture of an equilateral triangle.

• Find the length of the hypotenuse.

• Calculate the area of a triangle.

• Draw a picture of a square.

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

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

What does the altitude of an equilateral triangle create when drawn from the vertex to the base?

• A 60-degree angle

• A 120-degree angle

• A 45-degree angle

• A 90-degree angle

How do you find the small side of a 30-60-90 triangle if the medium side is known?

• Multiply by 2

• Multiply by √3

• Divide by 2

• Divide by √3

What is the significance of the 90-degree angle in the altitude of an equilateral triangle?

• It bisects the base.

• It bisects the vertex angle.

• It creates two 60-degree angles.

• It creates two 45-degree angles.

How do you find the medium side of a 30-60-90 triangle if the small side is known?

• Divide by √3

• Multiply by 2

• Divide by 2

• Multiply by √3

What is the length of the small side in a 30-60-90 triangle if the altitude is 18 cm?

• 18 cm

• 6 cm

• 9 cm

• 12 cm

What is the perimeter of an equilateral triangle if each side is 12√3?

• 24√3

• 60√3

• 36√3

• 48√3

What is the formula to find the perimeter of an equilateral triangle?

• 3 times the side length

• 2 times the side length

• Side length squared

• 4 times the side length

What is the perimeter of an equilateral triangle if the altitude is 18 cm?

• 108 cm

• 72 cm

• 54 cm

• 36 cm