How to use special right triangles to find the missing side lengths

The video tutorial explains the properties of a 45-45-90 triangle, highlighting that the sides are in a specific ratio. It discusses how to use the Pythagorean theorem to verify these properties but emphasizes the efficiency of using known relationships in special right triangles to simplify calculations. The tutorial concludes by underscoring the usefulness of these shortcuts in geometry.

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

• X

• X/2

• 2X

• X√2

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

• The hypotenuse is equal to one of the legs.

• The hypotenuse is half the length of one leg.

• The hypotenuse is twice the length of one leg.

• The hypotenuse is the length of one leg times √2.

How can the Pythagorean theorem be applied to a 45-45-90 triangle?

• By adding the squares of the legs and equating to the square of the hypotenuse.

• By subtracting the square of one leg from the hypotenuse.

• By multiplying the legs and dividing by the hypotenuse.

• By adding the legs and equating to the hypotenuse.

What is the square root of 50 simplified in terms of square roots?

• 5√2

• 10

• 25√2

• 50

Why are special right triangles like the 45-45-90 triangle useful?

• They are used in all types of triangles.

• They are easier to draw.

• They provide shortcuts for calculations.

• They have equal angles.