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

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

Yes, it forms a right triangle because 9² + 12² = 15² (81 + 144 = 225).

Front

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

Back

Use the Pythagorean Theorem: a² + b² = c². Rearrange the formula to find the missing side.

Front

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

Back

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

Front

What is the formula to calculate the distance between two points in a right triangle?

Back

The distance can be calculated using the Pythagorean Theorem: Distance = √(x² + y²), where x and y are the lengths of the two sides.

Front

In a right triangle, if one leg is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

12 (Using the Pythagorean Theorem: 5² + b² = 13², 25 + b² = 169, b² = 144, b = 12).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If a right triangle has legs of lengths 7 and 24, what is the length of the hypotenuse?

Back

25 (Using the Pythagorean Theorem: 7² + 24² = c², 49 + 576 = 625, c = 25).