8.1 Pythagorean Theorem & Its Converse In a right triangle, the square of the hypotenuse is equal to the sum of the squares of both legs. c a b.

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The Pythagorean Theorem and its Converse

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Presentation transcript:

8.1 Pythagorean Theorem & Its Converse

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of both legs. c a b

We usually use the letters a, b, and c to represent the lengths, with c being the hypotenuse. Formula 

Once we find the 3 side lengths of a triangle, and they are all whole numbers. That list of sides has a special name, they are called PYTHAGOREAN TRIPLES. i.e) c? 3 4

Common Groups of Pythagorean Triples 3,4,5 5,12,13 8,15,17 7,24,25 To find other triples you can take multiples of any known group. So take 3,4,5 and multiply each by 2 to get 6,8,10 as another triple.

When we solve for either a, b, or c we will take the square root of a value, remember when taking a square root you have a positive and a negative result. We can discard the negative result, but why?

Find c. c 14 9

4.5 6.3

4.5 6.3

Find the length of a leg Plug everything in that you know, and then solve the equation for the missing value.

Converse of the Pythagorean theorem If we can show that Then we know that we are dealing with a right triangle.

If a Triangle has side lengths 85, 84, and 13 If a Triangle has side lengths 85, 84, and 13. Is the triangle a right triangle? Which sides have to be a & b (your legs)?

You've just picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out?

The triangle is acute The triangle is obtuse If it is not a right triangle, then we can use the information found using the pythagorean theorem to know something about the triangle… The triangle is acute The triangle is obtuse