Triangle Properties and Relationships

The video tutorial covers two types of special right triangles: 45-45-90 and 30-60-90. It explains the properties of these triangles, including how to calculate the hypotenuse and legs using specific theorems. The tutorial provides examples to demonstrate the application of these properties in solving geometric problems, such as finding the height of an equilateral triangle and the distance of windshield wipers from the bottom of a windshield.

What is the measure of the two equal angles in a 45-45-90 triangle?

• 90°

• 60°

• 45°

• 30°

In a 45-45-90 triangle, how is the hypotenuse related to the legs?

• It is equal to the leg

• It is twice the leg

• It is the leg times √2

• It is the leg times √3

If one leg of a 45-45-90 triangle is 6, what is the length of the hypotenuse?

• 12√2

• 12

• 6√2

• 6

What theorem helps determine the third angle in a triangle?

• Base Angles Theorem

• Isosceles Triangle Theorem

• Triangle Sum Theorem

• Pythagorean Theorem

What is the measure of the smallest angle in a 30-60-90 triangle?

• 90°

• 30°

• 45°

• 60°

In a 30-60-90 triangle, how is the hypotenuse related to the shorter leg?

• It is the shorter leg times √3

• It is the shorter leg times √2

• It is twice the shorter leg

• It is equal to the shorter leg

If the shorter leg of a 30-60-90 triangle is 8, what is the length of the hypotenuse?

• 16√3

• 8√2

• 8

• 16

In a 30-60-90 triangle, how is the longer leg related to the shorter leg?

• It is equal to the shorter leg

• It is the shorter leg times √3

• It is twice the shorter leg

• It is the shorter leg times √2

What is the approximate height of an equilateral triangle with side length 32 mm?

• 32 mm

• 27.7 mm

• 55.4 mm

• 16 mm

How far from the bottom of the windshield are the ends of the wipers if they make a 60° angle?

• 12 in

• 20.8 in

• 24 in

• 30 in