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 are the legs of a right triangle?

Back

The legs of a right triangle are the two shorter sides that form the right angle.

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

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

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths (a² + b² = c²).

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a² + b² = c² for three lengths, then those lengths can form a right triangle.

Front

If the lengths are 9, 12, and 15, do they form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

Which lengths can form a right triangle: 6, 8, 10 or 5, 12, 13?

Back

Both sets can form a right triangle. For 6, 8, 10: 6² + 8² = 10² (36 + 64 = 100). For 5, 12, 13: 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Front

Can the lengths 10, 60, and 65 form a right triangle?

Back

No, because 10² + 60² does not equal 65² (100 + 3600 ≠ 4225).

Front

What is a right triangle?

Back

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