Pythagorean Theorem Review

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

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: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

What are the side lengths of a right triangle if the hypotenuse is 13 units and one side is 5 units?

Back

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

Front

Can a triangle with sides of lengths 2, 3, and 4 be a right triangle?

Back

No, because 2² + 3² = 4 + 9 = 13, which is not equal to 4² = 16.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

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

Front

What is the area of a right triangle with a base of 5 units and a height of 12 units?

Back

Area = (1/2) * base * height = (1/2) * 5 * 12 = 30 square units.

Front

What is the formula for the perimeter of a right triangle?

Back

Perimeter = a + b + c, where a and b are the lengths of the legs and c is the length of the hypotenuse.

Front

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

Back

Using the Pythagorean Theorem: 9² + b² = 15²; 81 + b² = 225; b² = 144; b = 12 units.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.