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 the length of a missing side, use the formula: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Tags

CCSS.8.G.B.7

Front

How do you find the length of a leg if you know the hypotenuse and the other leg?

Back

Rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

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 a leg.

Tags

CCSS.8.G.B.8

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8.

Tags

CCSS.8.G.B.7

Front

What is the importance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Tags

CCSS.8.G.B.8