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.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.8

Front

If one side of a right triangle is 3 feet and the other side is 4 feet, what is the length of the hypotenuse?

Back

5 feet (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Tags

CCSS.8.G.B.7

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.

Tags

CCSS.8.G.B.8

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 5-12-13 triangle?

Back

5, 12, and 13 are the side lengths of a right triangle, satisfying the Pythagorean Theorem: 5² + 12² = 13².

Tags

CCSS.8.G.B.8

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

What is the square root of 64?

Back

8 (The square root of a number is a value that, when multiplied by itself, gives the original number).

Tags

CCSS.8.EE.A.2

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is finding its square root.

Tags

CCSS.8.EE.A.2

Front

If a triangle has sides of lengths 4, 5, and 6, is it a right triangle?

Back

No, because 4² + 5² ≠ 6² (16 + 25 ≠ 36).

Tags

CCSS.8.G.B.8