The converse of the Pythagorean Theorem is also true. It allows you to prove that a triangle is a right triangle even if you do not know its angle measures.
Pythagorean Theorem Converse: If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
A combination of three numbers that makes the Pythagorean Theorem true is called a Pythagorean triple. Each set of numbers below is a Pythagorean triple.
Any multiple of a Pythagorean triple is also considered a Pythagorean triple. Multiplying 3, 4, 5 by 2 gives 6, 8, 10, which is another triple. To see if a set of numbers makes a Pythagorean triple, plug them into the Pythagorean Theorem.
What if you were told that a triangle had side lengths of 5, 12, and 13? How could you determine if the triangle were a right one?
What is the diagonal of a rectangle with sides 10 and 16?
Do 6, 7, and 8 make the sides of a right triangle?
Find the length of the hypotenuse.
Is 20, 21, 29 a Pythagorean triple?
Therefore, 20, 21, and 29 is a Pythagorean triple.
Determine if the triangles below are right triangles.
Find the length of the missing side. Simplify all radicals.
- If the legs of a right triangle are 10 and 24, then the hypotenuse is __________.
- If the sides of a rectangle are 12 and 15, then the diagonal is _____________.
- If the sides of a square are 16, then the diagonal is ____________.
- If the sides of a square are 9, then the diagonal is _____________.
Determine if the following sets of numbers are Pythagorean Triples.
- 12, 35, 37
- 9, 17, 18
- 10, 15, 21
- 11, 60, 61
- 15, 20, 25
- 18, 73, 75
Determine if the following lengths make a right triangle.
- 7, 24, 25
- 15, 20, 25
- 20, 25, 30
To see the Review answers, open this PDF file and look for section 8.2.