Pythagorean Theorem and Converse

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). Formula: a² + b² = c².

Front

What are the conditions for a triangle to be classified as a right triangle?

Back

A triangle is classified as a right triangle if one of its angles measures 90 degrees, and it satisfies the Pythagorean Theorem.

Front

How do you determine if a set of side lengths can form a right triangle?

Back

To determine if a set of side lengths can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides.

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which equals 5².

Front

What is the length of the hypotenuse if one side is 8 in and the other side is 15 in?

Back

The length of the hypotenuse is 17 in, calculated using the Pythagorean Theorem: √(8² + 15²) = √(64 + 225) = √289 = 17.

Front

What type of triangle is formed by sides of lengths 4, 5, and 6?

Back

The triangle is acute because 4² + 5² > 6² (16 + 25 > 36).

Front

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

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, which equals 25².

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle where one of the angles is greater than 90 degrees.