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: c² = a² + b².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

5 cm (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

In a right triangle, if the hypotenuse is 10 cm and one side is 6 cm, what is the length of the other side?

Back

8 cm (using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Front

True or False: The hypotenuse can be shorter than either of the other two sides in a right triangle.

Back

False.

Front

What is the formula to find the perimeter of a right triangle?

Back

The perimeter of a right triangle is the sum of the lengths of all three sides: P = a + b + c.

Front

If a right triangle has sides of length 5 cm and 12 cm, what is the length of the hypotenuse?

Back

13 cm (using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a right triangle has a hypotenuse of 15 cm and one side of 9 cm, what is the length of the other side?

Back

12 cm (using the Pythagorean Theorem: 15² = 9² + b²; 225 = 81 + b²; b² = 144; b = 12).

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.