Understanding 45-45-90 Triangles

This video tutorial covers the properties and significance of 45-45-90 triangles, a special type of right triangle. It explains why these triangles are unique, using the Pythagorean theorem to demonstrate their properties. The tutorial also covers rationalizing denominators, a common mathematical technique, and provides an example problem to illustrate the concepts discussed.

What makes a 45-45-90 triangle unique compared to other triangles?

• It has a 60-degree angle.

• It is an equilateral triangle.

• It has two equal angles.

• It has two equal sides.

In a 45-45-90 triangle, what is the measure of the two equal angles?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

What is the sum of the angles in any triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

How do you determine the length of the hypotenuse in a 45-45-90 triangle if one side is known?

• Divide the side by the square root of 2

• Divide the side by 2

• Multiply the side by the square root of 2

• Multiply the side by 2

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

• One leg is twice the other

• The legs are in a 1:2 ratio

• One leg is half the hypotenuse

• The legs are equal

What is the purpose of rationalizing the denominator in mathematical expressions?

• To convert fractions to decimals

• To make calculations easier

• To eliminate irrational numbers from the denominator

• To simplify the numerator

When rationalizing the denominator, what do you multiply the fraction by?

• The reciprocal of the fraction

• The numerator

• The denominator

• The square root of the denominator

Why might you not see your answer on a multiple-choice test if it involves a square root in the denominator?

• The answer is not simplified

• The answer is too complex

• The answer needs to be rationalized

• The answer is incorrect

In a 45-45-90 triangle, if one leg is 8, what is the length of the hypotenuse?

• 8

• 8√2

• 16

• 16√2

If the hypotenuse of a 45-45-90 triangle is 10, what is the length of each leg?

• 5√2

• 10√2

• 10/√2

• 5