Pythagorean Theorem: Find the Hypotenuse

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

How do you find the hypotenuse of a right triangle?

Back

To find the hypotenuse of a right triangle, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse, and a and b are the lengths of the other two sides.

Front

If Side A = 5 and Side B = 12, what is the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

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

Back

In a right triangle, the hypotenuse is always the longest side, and it is opposite the right angle.

Front

What is a right triangle?

Back

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

Front

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

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If the hypotenuse is 10 and one side is 6, how do you find the other side?

Back

Use the Pythagorean Theorem: a² + 6² = 10². Therefore, a² + 36 = 100, so a² = 64, and a = 8.

Front

What is the formula to calculate 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 are the common applications of the Pythagorean Theorem?

Back

The Pythagorean Theorem is commonly used in construction, navigation, physics, and various fields of engineering.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.