Pythagorean Theorem Review

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

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

True or False: A triangle with sides of lengths 5, 12, and 13 is a right triangle.

Back

True. This is a Pythagorean triple, satisfying the theorem: 5² + 12² = 13².

Tags

CCSS.8.G.B.8

Front

What is a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Example: (3, 4, 5).

Tags

CCSS.8.G.B.8

Front

How do 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 equals the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8

Front

Calculate the length of the diagonal of a rectangle with sides 6 cm and 8 cm.

Back

Using the Pythagorean Theorem: d² = 6² + 8² = 36 + 64 = 100. Therefore, d = √100 = 10 cm.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a right triangle and the angles?

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side. The other two sides are called legs.

Front

If one leg of a right triangle is 7 and the hypotenuse is 25, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 25² = 7² + b². So, 625 = 49 + b², thus b² = 576, and b = √576 = 24.

Tags

CCSS.8.G.B.7

Front

What is the formula for finding the area of a right triangle?

Back

The area of a right triangle is given by: Area = (1/2) × base × height.

Tags

CCSS.6.G.A.1