Properties of 30-60-90 and 45-45-90 Triangles

The video tutorial covers special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It explains the properties and formulas for these triangles, including how to calculate the hypotenuse and legs using the Pythagorean theorem. The tutorial provides examples to illustrate solving problems involving these triangles, emphasizing the importance of memorizing key formulas for efficient problem-solving.

What is the measure of each angle in a 45-45-90 triangle?

• 30°, 60°, 90°

• 45°, 45°, 90°

• 90°, 90°, 90°

• 60°, 60°, 60°

In a 45-45-90 triangle, if one leg is of length X, what is the length of the other leg?

• X

• 2X

• X√2

• X/2

Which theorem is used to find the hypotenuse in a 45-45-90 triangle?

• Cosine Rule

• Sine Rule

• Triangle Sum Theorem

• Pythagorean Theorem

If the legs of a 45-45-90 triangle are both X, what is the formula for the hypotenuse?

• X

• X/2

• 2X

• X√2

In a 45-45-90 triangle, if the hypotenuse is 5√2, what is the length of each leg?

• 5√2

• 5

• 10

• 2.5

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

• 45°

• 30°

• 90°

• 60°

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

• Equilateral triangles

• 30-60-90 triangles

• 45-45-90 triangles

• Scalene 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

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

• X/2

• X

• 2X

• X√3

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the short leg?

• 6√3

• 6

• 12

• 3