Pythagorean Theorem

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: c² = a² + b².

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 are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Tags

CCSS.8.G.B.7

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Tags

CCSS.8.G.B.7

Front

How do you find the length of a leg if the hypotenuse is 10 and the other leg is 6?

Back

Using the formula: a² = c² - b²; a² = 10² - 6²; a² = 100 - 36; a² = 64; a = 8.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

Using the formula: b² = c² - a²; b² = 13² - 5²; b² = 169 - 25; b² = 144; b = 12.

Tags

CCSS.8.G.B.7

Front

What is the converse of the Pythagorean Theorem?

Back

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

Tags

CCSS.8.G.B.8