Pythagorean Theorem and Special Right Triangles

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). Formula: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is the opposite operation of squaring a number.

Tags

CCSS.8.EE.A.2

Front

In a 45-45-90 triangle, what is the ratio of the lengths of the legs to the hypotenuse?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 5?

Back

In a 30-60-90 triangle, the hypotenuse is twice the length of the shorter leg. Therefore, the hypotenuse is 10.

Tags

CCSS.8.G.B.8

Front

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

Back

In a right triangle, the side opposite the right angle is the longest side, known as the hypotenuse, and is always longer than either of the other two sides.

Front

If one leg of a right triangle is 6 and the other leg 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 value of x in a 45-45-90 triangle with legs of length 4?

Back

In a 45-45-90 triangle, the hypotenuse is 4√2.

Tags

CCSS.8.G.B.8

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

What is the formula to find the area of a right triangle?

Back

Area = 1/2 * base * height.

Tags

CCSS.6.G.A.1

Front

If the hypotenuse of a right triangle is 13 and one leg is 5, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = 12.

Tags

CCSS.8.G.B.7