Pythagorean Theorem & Converse and Triangle Inequalities

Front

What is the Pythagorean Theorem?

Back

Front

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

Back

To determine if three lengths can form a triangle, the Triangle Inequality Theorem states that 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

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

Front

What is an obtuse triangle?

Back

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

Front

What is a right triangle?

Back

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

Front

If a triangle has sides of lengths 5 and 5, what is a possible length for the third side?

Back

The possible length for the third side must be less than the sum of the two equal sides (5 + 5 = 10) and greater than the difference (5 - 5 = 0). Therefore, a possible length is 9.

Front

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

Back

Front

What is the Converse of the Pythagorean Theorem?

Back

The Converse of the Pythagorean Theorem states that 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

How do you find the missing leg of a right triangle?

Back

Front

What is the range for the length of the third side of a triangle with sides of lengths 8 and 10?

Back

The length of the third side must be greater than the difference of the two sides (10 - 8 = 2) and less than the sum of the two sides (10 + 8 = 18). Therefore, the range is (2, 18).