1. 7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE
GEOMETRY

2. Pythagorean Theorem (Thm
Pythagorean Theorem (Thm. 7-4): In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
𝑎 2 + 𝑏 2 = 𝑐 2

3. Pythagorean Triple: set of nonzero whole numbers, a, b, and c that satisfy the Pythagorean Theorem
Common Triples:
3, 4, , 12, 13
7, 24, , 15, 17
12, 25, , 21, 29

4. Ex. 1) Are 6, 8, and 15 a Pythagorean Triple?

5. Ex. 2) Find the variable.

6. Ex. 3) Find the variable.

7. Ex. 4) Find the variable.

8. Ex. 5) Finding the Area using the Pythagorean Thm.

9. 𝑎 2 + 𝑏 2 = 𝑐 2 𝑎 2 + 𝑏 2 > 𝑐 2 𝑎 2 + 𝑏 2 < 𝑐 2
Converse of the Pythagorean Theorem (Thm. 7-5): If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
𝑎 2 + 𝑏 2 = 𝑐 2
𝑎 2 + 𝑏 2 > 𝑐 2
𝑎 2 + 𝑏 2 < 𝑐 2
Right Triangle
Acute Triangle
Obtuse Triangle

10. Ex. 6) Classify the triangle.

11. Ex. 7)