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 is expressed as: a² + b² = c².

Front

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

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If a = 5 and b = 12, what is c?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is a right triangle?

Back

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

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If a = 6 and c = 10, what is b?

Back

b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What does 'a' and 'b' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs (the sides that form the right angle) of a right triangle.

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 are in the ratio 3:4:5, which satisfies the Pythagorean Theorem: 3² + 4² = 5².

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, it is a right triangle because 8² + 15² = 17² (64 + 225 = 289).

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.