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 are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. Additionally, it must satisfy the Pythagorean Theorem.

Front

If the lengths of two sides of a right triangle are 9 and 12, what is the length of the hypotenuse?

Back

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

Front

Do the segment lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

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 right triangle has side lengths 6, 6.7, and 3, which side is the hypotenuse?

Back

The hypotenuse is 6.7, as it is the longest side.

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

Find the length of the missing side if one side is 5 and the hypotenuse is 13.

Back

Using the Pythagorean Theorem: 5² + b² = 13². Therefore, 25 + b² = 169, so b² = 144, and b = 12.

Front

What is the distance between two points in a coordinate plane?

Back

The distance can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If one side of a right triangle is 8 and the hypotenuse is 10, what is the length of the other side?

Back

Using the Pythagorean Theorem: 8² + b² = 10². Therefore, 64 + b² = 100, so b² = 36, and b = 6.