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

How do you determine if three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Front

What type of triangle is formed by lengths 2, 3, and 5?

Back

Not a Triangle. The lengths do not satisfy the Triangle Inequality Theorem.

Front

Do the lengths 15, 12, and 9 form a right triangle?

Back

Yes. They satisfy the Pythagorean Theorem: 15² = 12² + 9².

Front

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

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

10. Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is a right triangle?

Back

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

Front

How can you classify a triangle with sides 8, 15, and 17?

Back

Right triangle. It satisfies the Pythagorean Theorem: 17² = 8² + 15².

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, one angle is 90 degrees, and the sum of the other two angles is 90 degrees.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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