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 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 12 cm and the other side is 9 cm, what is the length of the hypotenuse?

Back

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

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

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 a ladder is placed 10 feet away from a wall and needs to reach a height of 25 feet, how long must the ladder be?

Back

Using the Pythagorean Theorem: c² = 10² + 25² = 100 + 625 = 725. Therefore, c = √725 ≈ 26.93 feet, which rounds to 27 feet.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25).

Front

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

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

Front

If the lengths of two sides of a right triangle are 8 in. and 15 in., what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 in.

Front

What is a right triangle?

Back

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