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). It can be expressed as: a² + b² = c².

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a² + b² = c² for a triangle, then the triangle is a right triangle.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side lengths must satisfy the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

Do the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

Do the lengths 6, 8, and 10 form a right triangle?

Back

Yes, because 6² + 8² = 10² (36 + 64 = 100).

Front

What type of triangle has one right angle?

Back

A right triangle has one right angle (90 degrees).

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.