Pythagorean Theorem Practice 12/12

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

In a right triangle, which angle is opposite the hypotenuse?

Back

The right angle (90 degrees) is opposite the hypotenuse.

Front

What are the two legs of a right triangle?

Back

The two legs of a right triangle are the sides that form the right angle.

Front

How do you find the length of one leg if you know the hypotenuse and the other leg?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

If the hypotenuse of a right triangle is 10 units and one leg is 6 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8 units.