Pythagorean Theorem Converse

Front

What is the Pythagorean Theorem?

Back

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 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

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 do you determine if a triangle with sides 7, 24, and 25 is a right triangle?

Back

Check if 7² + 24² = 25². Since 49 + 576 = 625, it is a right triangle.

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 9, 12, and 15, do they form a right triangle?

Back

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

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 shorter sides equals the square of the longest side.

Front

If a triangle has sides 13, 80, and 81, does it form a right triangle?

Back

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

Front

What is a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What is the formula to find the hypotenuse?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.