PointsComplete the proof of the Pythagorean theorem. Given: △ is a right triangle, with

a right angle at ∠.

Prove: a^2 +b^2 =c ^2



Statement Reason

1. △ ABC is a right triangle, with a right angle

at ∠C.

1. Given

2. Draw an altitude from point C to. 2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.

3. ∠CDB and ∠CDA are right angles. 3. Definition of altitude

4. ∠BCA ≅ ∠BDC 4. All right angles are congruent.

5. ∠B ≅ ∠B 5.

6. 6. AA Similarity Postulate

7.a/x =c/a
7.

8. a^2= cx 8.

9. ∠ CDA≅ ∠BCA 9.

10. ∠A ≅ ∠A 10.

11. 11. AA Similarity Postulate

Statement/ Reason

12. b/y=c/b= 12.

13. b^2 =cy 13.

14. a^2+b^2=cx+cy 14.
15. 15. Distributive Property

16.x+y=c 16.

17. a^2+b^2=c^2 17.