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). It can be expressed as: a² + b² = c².

Front

What is a right triangle?

Back

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

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.

Front

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

Back

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

Front

What is the distance formula?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).

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

Do the lengths 13, 80, and 81 form a right triangle?

Back

No, because 13² + 80² ≠ 81² (169 + 6400 ≠ 6561).

Front

Given the lengths 6 in, 8 in, and 10 in, do they form a right triangle?

Back

Yes, because 6² + 8² = 10² (36 + 64 = 100).

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

If one side of a right triangle is 5 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.