Pythagorean Theorem (Finding the Hypotenuse)

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 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 6 cm and the other side is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 cm.

Front

What is the formula to find the hypotenuse using the Pythagorean Theorem?

Back

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

Front

If the hypotenuse of a right triangle is 13 cm and one side is 5 cm, what is the length of the other side?

Back

Using the Pythagorean Theorem: 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12 cm.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

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

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem is specific to right triangles.

Front

If a right triangle has legs of lengths 9 cm and 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12²; c² = 81 + 144; c² = 225; c = 15 cm.

Front

What is the value of the hypotenuse if both legs of a right triangle are equal to 1 cm?

Back

Using the Pythagorean Theorem: c² = 1² + 1²; c² = 1 + 1; c² = 2; c = √2 cm.

Front

If a right triangle has a hypotenuse of 20 cm and one leg of 15 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 20² = 15² + b²; 400 = 225 + b²; b² = 175; b = √175 cm or approximately 13.23 cm.