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

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

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 the sides of a triangle are 5, 12, and 13, do they form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

If the sides of a triangle are 8, 15, and 17, do they form a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289 = 17².

Front

If the sides of a triangle are 7, 24, and 25, do they form a right triangle?

Back

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

Front

If the sides of a triangle are 10, 10, and 14, do they form a right triangle?

Back

No, because 10² + 10² = 100 + 100 = 200, which is not equal to 14² (196).

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

What is an example of a set of side lengths that do not form a right triangle?

Back

The side lengths 20, 21, and 22 do not form a right triangle because 20² + 21² = 400 + 441 = 841, which is not equal to 22² (484).