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 the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

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, and it satisfies the Pythagorean Theorem.

Front

Which set of numbers can represent the sides of a right triangle? 5, 12, 13 or 8, 10, 12?

Back

The set 5, 12, 13 can represent the sides of a right triangle because it satisfies the Pythagorean Theorem: 5² + 12² = 13².

Front

How can you determine if a set of 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 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, where the shortest side is opposite the 30-degree angle.

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 length of the hypotenuse is √2 times the length of each leg.

Front

If the hypotenuse of a right triangle is 10 cm and one side is 6 cm, what is the length of the other side?

Back

The length of the other side is 8 cm, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a² + b² = c² for three lengths, then those lengths can form a right triangle.