Pythagorean Theorem converse

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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

Yes, it forms a right triangle because 9² + 12² = 15² (81 + 144 = 225).

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

Given sides a = 2.1, b = 7.2, and c = 7.5, is this a right triangle?

Back

Yes, it is a right triangle because 2.1² + 7.2² = 7.5² (4.41 + 51.84 = 56.25).

Front

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

Back

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

Front

If the sides of a triangle are 9, 40, and 41, which side is the hypotenuse?

Back

The hypotenuse is 41.

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 obtuse triangles?

Back

No, the Pythagorean Theorem cannot be used for obtuse triangles.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

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