1. Pythagorean Theorem

2. Review

3. c² = a² + b²
25 =

4. Pythagorean Theorem
A right triangle is a triangle with a 90° angle.

5. Pythagorean Theorem The angles in any triangle add up to 180°.
In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.
Explain this reasoning (Think Pair Share)

6. Pythagorean Theorem
In a right triangle, the side opposite the 90° angle is called the hypotenuse and the remaining two sides are called the legs.
Hypotenuse
Leg
Leg

7. Pythagorean Theorem
Question: Suppose that two angles in a triangle are 60° and 30°. Is it a right triangle?
Solution: Yes. The third angle must be
180° - 60° - 30° = 90°.

8. Pythagorean Theorem
Question: Suppose that a triangle has a 100° angle. Is it a right triangle? Answer YES, NO, or MAYBE.
Solution: No. The remaining two angles must sum to 80°, so neither remaining angle is a 90° angle.

9. Pythagorean Theorem
Question: Suppose that a triangle has a 70° angle. Is it a right triangle? Answer YES, NO, or MAYBE.
Solution: Maybe. The remaining two angles must sum to 110°, so one of the remaining angles could be a 90° angle.

10. Pythagorean Theorem
Question: Suppose that two angles in a triangle are 80° and 40°. Is it a right triangle?
Solution: No. The third angle must be
180° - 80° - 40° = 60°.

11. Pythagorean Theorem
the sum of the squares of the shorter sides is equal to the square of the hypotenuse.
if a triangle has this kind of relationship between the lengths of its sides, then it must be a right triangle!

12. Pythagorean Theorem
c² = a² + b²

13. Pythagorean Theorem
Question: Suppose the legs of a right triangle have lengths  8  and  6  , Find the hypotenuse
Solution: = x = x = x2
√100 = √x x = 10

14. Pythagorean Theorem
Question: Suppose the legs of a right triangle have lengths  3  and   6 , Find the hypotenuse
Solution: = x = x = x x = ~ 6.7

15. Pythagorean Theorem
Question: Suppose the legs of a right triangle have lengths  3  and   x , and the hypotenuse has length   5 . Find   x .
Solution: x2 = x2 = x2 = 16
√x2 = √ x = 4

16. Pythagorean Theorem
Question: Suppose the legs of a right triangle have lengths  4  and   x , and the hypotenuse has length   7 . Find   x .
Solution: x2 = x2 = x2 = 33
√x2 = √ x = ~5.74

18. Pythagorean Theorem Summary c2 = a2 + b2 (if looking for hypotenuse)
c2 - a2 = b2 (if have hypotenuse)
Workout
Complete Worksheet
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