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 is 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

To find the length of the hypotenuse (c), use the formula: c = √(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

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

Back

The length of the hypotenuse is 5, calculated using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.8.G.B.7

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c).

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The sides 5, 12, and 13 form a right triangle, satisfying the Pythagorean Theorem: 5² + 12² = 13².

Tags

CCSS.8.G.B.8

Front

If the lengths of the legs of a right triangle are both equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Tags

CCSS.4.G.A.2

Front

What is the length of the missing side if one leg is 6 and the hypotenuse is 10?

Back

The length of the missing side is 8, calculated using the Pythagorean Theorem: a = √(c² - b²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

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 such that a² + b² = c², then the triangle is a right triangle.

Tags

CCSS.8.G.B.8