Converse of Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

What is a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What is the Pythagorean Theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

Use the Converse of the Pythagorean Theorem: check if a² + b² = c² for the longest side c.

Front

What are the side lengths of a right triangle?

Back

The side lengths must satisfy the Pythagorean theorem: a² + b² = c².

Front

Which of the following sets of lengths form a right triangle: 5, 12, 13?

Back

Yes, because 5² + 12² = 13² (25 + 144 = 169).

Front

Which set of lengths does not form a right triangle: 8, 15, 20?

Back

No, because 8² + 15² ≠ 20² (64 + 225 ≠ 400).

Front

What is the longest side of a right triangle called?

Back

The hypotenuse.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).