Pythagorean Theorem Flashcard

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 longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

If the hypotenuse is 10 units and one side is 6 units, how do you find the other side?

Back

Use the formula: b² = c² - a²; b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8 units.

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1:√3:2.

Front

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

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).