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 the hypotenuse in a right triangle?

Back

The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of the triangle.

Front

If one leg of a right triangle is 5 and the other leg is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13.

Tags

CCSS.8.G.B.7

Front

Find the length of the missing side if one leg is 9 and the hypotenuse is 15.

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 15² = 9² + b². So, 225 = 81 + b². Thus, b² = 144, and b = √144 = 12.

Tags

CCSS.8.G.B.7

Front

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

Back

To find the length of a leg (a or b) in a right triangle, use the formula: a² = c² - b² or b² = c² - a², where c is the hypotenuse.

Tags

CCSS.8.G.B.7

Front

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

Back

Using the Pythagorean Theorem: 10² = 6² + b². So, 100 = 36 + b². Thus, b² = 64, and b = √64 = 8.

Tags

CCSS.8.G.B.7

Front

What are the conditions for using the Pythagorean Theorem?

Back

The Pythagorean Theorem can only be used in right triangles, where one angle measures 90 degrees.

Tags

CCSS.8.G.B.8

Front

If a right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem: 5² = 3² + 4².

Tags

CCSS.8.G.B.8

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8