4.5 Pythagorean Theorem 8.6C, 8.7C D

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 is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 x 4 = 16.

Tags

CCSS.8.EE.A.2

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

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.

Front

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

Back

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

Tags

CCSS.8.G.B.7

Front

What is the approximate value of √50?

Back

7 (Since 7² = 49 and 8² = 64, √50 is between 7 and 8, closer to 7).

Tags

CCSS.8.NS.A.2

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle.

Tags

CCSS.HSG.CO.C.10

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 hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

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

Back

12 cm (Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Tags

CCSS.8.G.B.7

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