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.

Tags

CCSS.8.G.B.8

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.2

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

If a triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

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

Tags

CCSS.8.G.B.8

Front

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

Back

Use the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a right triangle if the hypotenuse is 41 and one side is 40?

Back

The other side can be found using the Pythagorean Theorem: 41² - 40² = 9, so the side lengths are 9, 40, and 41.

Tags

CCSS.8.G.B.8

Front

What does it mean if a triangle is not a right triangle?

Back

It means that the triangle does not satisfy the Pythagorean Theorem; the square of the longest side is not equal to the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8

Front

Can a triangle with sides 13, 80, and 81 be a right triangle?

Back

No, because 13² + 80² = 169 + 6400 = 6569, which is not equal to 81² (6561).

Tags

CCSS.8.G.B.8

Front

What is the converse of the Pythagorean Theorem?

Back

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

Tags

CCSS.8.G.B.8

Front

If a triangle has sides 2.1, 7.2, and 7.5, is it a right triangle?

Back

Yes, because 2.1² + 7.2² = 7.5² (4.41 + 51.84 = 56.25).

Tags

CCSS.8.G.B.8