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). Formula: a² + b² = c².

Front

What is the formula for the Pythagorean Theorem?

Back

a² + b² = c²

Front

If one side of a right triangle is 6 units and the other side is 8 units, what is the length of the hypotenuse?

Back

10 units (Using the Pythagorean Theorem: 6² + 8² = c² => 36 + 64 = c² => 100 = c² => c = 10).

Front

What does the Pythagorean Theorem help to find?

Back

It helps to find the length of a missing side in a right triangle.

Front

What is the opposite operation of squaring a number?

Back

Square root.

Front

In a right triangle, if the lengths of the two legs are 3 and 4, what is the length of the hypotenuse?

Back

5 (3² + 4² = 5² => 9 + 16 = 25).

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

Right triangles.

Front

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

Back

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

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.