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 a right triangle?

Back

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

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle with sides a, b, and c is a right triangle, check if a² + b² = c², where c is the longest side.

Front

What are the side lengths of a 3-4-5 triangle?

Back

The side lengths of a 3-4-5 triangle are 3, 4, and 5, which satisfy the Pythagorean Theorem (3² + 4² = 5²).

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

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

Front

What type of triangle has all angles less than 90 degrees?

Back

An acute triangle.

Front

What type of triangle has one angle greater than 90 degrees?

Back

An obtuse triangle.

Front

Which set of sides can form a right triangle: 5, 12, 13 or 8, 15, 17?

Back

Both sets can form right triangles. 5² + 12² = 13² and 8² + 15² = 17².

Front

What is the area of a square with a side length of 9 feet?

Back

The area of a square is calculated as side length squared. So, area = 9² = 81 square feet.

Front

If a ladder is 10 feet long and the base is 4 feet from the wall, how high does it reach on the wall?

Back

Using the Pythagorean Theorem: 10² = 4² + h²; 100 = 16 + h²; h² = 84; h = √84 ≈ 9.17 feet.