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: c² = a² + b².

Front

What are the side lengths of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

What are the side lengths 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, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.

Front

How can you determine if a set of numbers can form a right triangle?

Back

To determine if a set of numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers (c² = a² + b²).

Front

What is the range of possible lengths for the third side of a triangle with sides of lengths a and b?

Back

The range of possible lengths for the third side (c) must satisfy the triangle inequality: |a - b| < c < a + b.

Front

If one leg of a 45-45-90 triangle is 10 cm, what is the length of the hypotenuse?

Back

The hypotenuse is 10√2 cm.

Front

In a 30-60-90 triangle, if the shorter leg is 5 cm, what is the length of the longer leg?

Back

The longer leg is 5√3 cm.

Front

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

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: c² = a² + b².

Front

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

Back

To find the length of a missing side, use the Pythagorean Theorem: rearrange the formula to solve for the unknown side.

Front

What is the value of the hypotenuse in a right triangle with legs of lengths 6 cm and 8 cm?

Back

The hypotenuse is 10 cm (using the Pythagorean Theorem: 10² = 6² + 8²).