Pythagorean Theorem 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.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: 3² + 4² = c², so 9 + 16 = c², thus c = 5).

Front

Find the length of the missing side if a = 6 and c = 10.

Back

b = 8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b² = 64, and b = 8).

Front

What is the formula to find the length of a side in a right triangle?

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c².

Front

If c = 15 and b = 9, what is a?

Back

a = 12 (Using the Pythagorean Theorem: a² + 9² = 15², so a² + 81 = 225, thus a² = 144, and a = 12).

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

If a = 8 and c = 10, what is b?

Back

b = 6 (Using the Pythagorean Theorem: 8² + b² = 10², so 64 + b² = 100, thus b² = 36, and b = 6).

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

The hypotenuse is 13 (Using the Pythagorean Theorem: 5² + 12² = c², so 25 + 144 = c², thus c = 13).