Pythagorean Theorem

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.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the side opposite the right angle in a right triangle and is the longest side.

Front

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

Back

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

Front

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

Back

Use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The diagonal (d) can be calculated using the Pythagorean Theorem: d = √(length² + width²).

Front

In a right triangle with sides 6, 8, and 10, which side is the hypotenuse?

Back

10 (It is the longest side in the triangle).

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.

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.

Front

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

Back

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

Front

What is the area of a right triangle with base 6 and height 8?

Back

24 (Area = 1/2 * base * height = 1/2 * 6 * 8).