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 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 9 and the other is 40, what is the length of the hypotenuse?

Back

c = 41 (using the Pythagorean Theorem: 9² + 40² = c²).

Front

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

Back

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

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

Find the missing side if a = 6 and c = 10.

Back

b = 8 (using the Pythagorean Theorem: 6² + b² = 10²).

Front

What do the letters a, b, and c represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, a and b represent the lengths of the two legs of the right triangle, and c represents the length of the hypotenuse.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, it is a right triangle because 3² + 4² = 5².

Front

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

Back

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

Front

Calculate the hypotenuse if the legs are 8 and 15.

Back

c = 17 (using the Pythagorean Theorem: 8² + 15² = c²).