8.GSR.8.1 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). 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

What is the hypotenuse of 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

Which set of sides forms a right triangle: 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13 forms a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

If the sides of a triangle are 6 in, 8 in, and 10 in, does it form a right triangle?

Back

Yes, it forms a right triangle because 6² + 8² = 10² (36 + 64 = 100).

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

If a triangle has sides of lengths 9, 40, and 41, which side is the hypotenuse?

Back

The hypotenuse is 41, as it is the longest side.

Front

Can a triangle with sides 5, 10, and 12 be a right triangle?

Back

No, it cannot be a right triangle because 5² + 10² ≠ 12² (25 + 100 ≠ 144).

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.