Converse of Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

What is a right triangle?

Back

A triangle in which one of the angles measures 90 degrees.

Front

What is the Pythagorean Theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

How can you determine if three lengths can form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is an acute triangle?

Back

A triangle in which all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

A triangle in which one of the angles is greater than 90 degrees.

Front

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

Back

It is a right triangle, because 3² + 4² = 5².

Front

If a triangle has sides of lengths 5, 5, and 8, can it be a triangle?

Back

Yes, because 5 + 5 > 8.

Front

If a triangle has sides of lengths 7, 8, and 10, what type of triangle is it?

Back

It is an acute triangle, because 7² + 8² > 10².

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.