Pythagorean Theorem & 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 is expressed as: c² = a² + b².

Front

What is a right triangle?

Back

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

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If a triangle has sides of lengths 4, 5, and 6, is it acute, obtuse, or right?

Back

The triangle is acute.

Front

If the legs of a right triangle are 10 and 24, what is the length of the hypotenuse?

Back

The hypotenuse is 26.

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

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

Back

If a² + b² = c² holds true for the lengths of the sides, then the triangle is a right triangle.

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

If a = 2.1, b = 7.2, and c = 7.5, is this a right triangle?

Back

Yes, it is a right triangle.