Pythagorean 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 is a right triangle?

Back

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

Front

What are the side lengths of a right triangle called?

Back

The side lengths of a right triangle are called legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

How can you determine if three side lengths form a right triangle?

Back

To determine if three side lengths (a, b, c) form a right triangle, check if a² + b² = c², where c is the longest side.

Front

Do the side lengths 12, 20, 16 form a right triangle?

Back

Yes, because 12² + 16² = 144 + 256 = 400 = 20².

Front

Solve for c: If a = 5 and b = 12, what is c?

Back

c = 13, because 5² + 12² = 25 + 144 = 169, and √169 = 13.

Front

Do the side lengths 4, 4, 4 form a right triangle?

Back

No, because all sides are equal and do not satisfy the Pythagorean theorem.

Front

Do the side lengths 7, 24, 25 form a right triangle?

Back

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

Front

Do the side lengths 20, 13, 29 form a right triangle?

Back

No, because 20² + 13² = 400 + 169 = 569, which is not equal to 29² (841).

Front

What is the hypotenuse in a right triangle?

Back

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