Pythagorean Theorem and special right triangles practice

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 a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

In a 45-45-90 triangle, what is the relationship between the legs and the hypotenuse?

Back

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

Front

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 5?

Back

The length of the hypotenuse is 5√2, which is approximately 7.07.

Front

In a 30-60-90 triangle, what is the relationship between the sides?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the shorter side.

Front

What is the length of the hypotenuse in a 30-60-90 triangle with the shorter leg measuring 4?

Back

The length of the hypotenuse is 8.

Front

How do you find the missing side of a right triangle using the Pythagorean Theorem?

Back

To find a missing side, rearrange the Pythagorean Theorem formula: c² = a² + b². If you know two sides, you can solve for the third.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

What is a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides have different lengths.