Properties of Equilateral Triangles and Rotations

The video tutorial covers various geometric concepts, including properties of equilateral triangles, calculating triangle areas, and understanding 45-45-90 triangles. It also explains how to find the diagonal of a square, explores the relationship between ramp angles and distances, and discusses parallel segments and scale factors. Additionally, the tutorial delves into triangle rotations and identifying centers of rotation.

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

• 120°

• 90°

• 45°

• 60°

In an equilateral triangle, if one side is 6 units, what is the length of the altitude?

• 3

• 6

• 6√3

• 3√3

How do you calculate the area of an equilateral triangle with side length 10?

• 25√3

• 50√3

• 10²

• 10√3

What is the relationship between the hypotenuse and a leg in a 45-45-90 triangle?

• Hypotenuse is half a leg

• Hypotenuse is √2 times a leg

• Hypotenuse is twice a leg

• Hypotenuse is equal to a leg

If a square has a side length of 3 units, what is the length of its diagonal?

• 3√2

• 6

• 9

• 3

What happens to the angle a ramp makes with the ground if the ramp is moved further from the step?

• The angle remains the same

• The angle becomes 90°

• The angle decreases

• The angle increases

If segment A'B' is parallel to segment AB and the scale factor is 1/3, what is the length of A'B' if AB is 12 units?

• 8

• 6

• 4

• 12

Which point remains unchanged in a 60° clockwise rotation around point O?

• Point G

• Point P

• Point O

• Point A