Practice Pythagorean Theorem Test

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 the diagonal of a rectangular box?

Back

To find the length of the diagonal (d) of a rectangular box, use the formula: d = √(l² + w² + h²), where l is the length, w is the width, and h is the height of the box.

Tags

CCSS.8.G.B.7

Front

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

Back

Using the Pythagorean Theorem: c = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.

Tags

CCSS.8.G.B.7

Front

What is the square root of 144?

Back

The square root of 144 is 12.

Tags

CCSS.8.EE.A.2

Front

In a right triangle, if one angle is 90 degrees and the other two angles are 30 degrees and 60 degrees, what are the ratios of the sides?

Back

The ratios of the sides opposite the 30°, 60°, and 90° angles are 1:√3:2.

Tags

CCSS.HSG.SRT.C.8

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 length of the hypotenuse is √2 times the length of one leg.

Tags

CCSS.8.G.B.8

Front

How do you calculate the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) × base × height.

Tags

CCSS.6.G.A.1

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?

Back

The distance (d) between two points is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

If the diagonal of a rectangle is 10 cm and one side is 6 cm, how do you find the other side?

Back

Use the Pythagorean Theorem: c² = a² + b². Here, 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = 8 cm.

Tags

CCSS.8.G.B.8

Front

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Tags

CCSS.8.EE.A.2