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: c² = a² + b².

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c). The hypotenuse is the longest side, opposite the right angle.

Front

How can you determine if a set of numbers represents the sides of a right triangle?

Back

To determine if a set of numbers represents the sides of a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers. If c² = a² + b², then it is a right triangle.

Front

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

Back

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

Front

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

Back

In a right triangle, the hypotenuse is always longer than either leg, and the relationship is defined by the Pythagorean Theorem: c² = a² + b².

Front

What is the value of the hypotenuse if one leg is 5 and the other leg is 12?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

What does it mean if a triangle is not a right triangle?

Back

If a triangle is not a right triangle, it does not have a 90-degree angle, and the Pythagorean Theorem does not apply.

Front

What are the possible labels for the legs of a right triangle?

Back

The legs of a right triangle can be labeled as 'a' and 'b'.

Front

If the hypotenuse is 15 and one leg is 9, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b²; 15² = 9² + b²; 225 = 81 + b²; b² = 144; b = 12.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height, where the base and height are the lengths of the legs.