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). It can be expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = c², 9 + 16 = c², 25 = c², c = 5).

Front

What is the longest side of a right triangle called?

Back

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

Front

In the equation a² + b² = c², what do a and b represent?

Back

In the equation, a and b represent the lengths of the two legs (the shorter sides) of the right triangle.

Front

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

Back

The relationship is defined by the Pythagorean Theorem: the sum of the squares of the two shorter sides equals the square of the longest side.

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: a² + b² = c², and solve for the unknown side.

Front

What is the final step in solving for c in the equation 25 = c²?

Back

The final step is to take the square root of both sides: c = √25, so c = 5.

Front

What is a right angle?

Back

A right angle is an angle that measures exactly 90 degrees.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is significant because it is the longest side and is opposite the right angle.