Pythagorean Theorem

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

In a right triangle, which side is the longest?

Back

The hypotenuse is the longest side in a right triangle.

Front

If a triangle has sides of lengths 10, 12, and 15, how would you classify it?

Back

The triangle is classified as obtuse because 15² > 10² + 12².

Front

If a triangle has sides of lengths 6, 9, and 15, how would you classify it?

Back

The triangle is classified as acute because 15² < 6² + 9².

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If one side of a right triangle is 20 in and the other is 48 in, what is the length of the hypotenuse?

Back

The hypotenuse is 52 in, calculated using the Pythagorean Theorem: c = √(20² + 48²) = √(400 + 2304) = √2704 = 52.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is an example of a Pythagorean triple?

Back

An example of a Pythagorean triple is (3, 4, 5), where 3² + 4² = 5².

Front

How do you determine if a triangle is right-angled using side lengths?

Back

To determine if a triangle is right-angled, check if the square of the longest side equals the sum of the squares of the other two sides.