Pythagorean Theorem Test 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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. Rearrange the formula a² + b² = c² to solve for the missing side.

Tags

CCSS.8.G.B.7

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Tags

CCSS.8.G.B.7

Front

What is the distance formula used for?

Back

The distance formula is used to find the distance between two points in a coordinate plane. It is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

Do the lengths 15, 12, and 9 form a right triangle?

Back

Yes, they do. Check using the Pythagorean Theorem: 15² = 12² + 9² (225 = 144 + 81).

Tags

CCSS.8.G.B.8

Front

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

Back

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

Front

If a right triangle has legs of lengths 5 and 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

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

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and computer graphics, to calculate distances and ensure structures are built correctly.

Tags

CCSS.8.G.B.8

Front

How can you determine if a triangle is a right triangle?

Back

To determine if a triangle is a right triangle, check if the lengths of the sides satisfy the Pythagorean Theorem: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the hypotenuse in a right triangle?

Back

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