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 type of triangles does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

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, so C = √25 = 5).

Front

What is the formula to find the length of the hypotenuse?

Back

C = √(A² + B²) where C is the hypotenuse and A and B are the other two sides.

Front

If A = 5 and B = 12, what is C?

Back

C = 13 (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169, so C = √169 = 13).

Front

How do you find the length of one side if you know the hypotenuse and one other side?

Back

You can rearrange the Pythagorean Theorem: A = √(C² - B²) or B = √(C² - A²).

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

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

6 (Using the Pythagorean Theorem: 10² - 8² = 100 - 64 = 36, so the other leg = √36 = 6).

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.