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 defines an acute triangle?

Back

A triangle where all three interior angles are less than 90 degrees.

Front

What defines an obtuse triangle?

Back

A triangle that has one interior angle greater than 90 degrees.

Front

What defines a right triangle?

Back

A triangle that has one interior angle equal to 90 degrees.

Front

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

Back

Right triangle, because 3² + 4² = 5².

Front

If a triangle has sides of lengths 2, 2, and 3, can these be the measures of a triangle?

Back

Yes, because the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is the relationship between the sides of an acute triangle?

Back

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.

Front

What is the relationship between the sides of an obtuse triangle?

Back

In an obtuse triangle, the square of the longest side is greater than the sum of the squares of the other two sides.

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.

Front

Can a triangle have sides of lengths 5, 12, and 13?

Back

Yes, it is a right triangle because 5² + 12² = 13².