+4 Complete the proof of the Pythagorean theorem.
Given: triangle ABC is a right triangle, with a right angle at angel c
Prove: a2+b2=c2
1. triangle ABC is a right triangle, with a right angle C 1. Given
2. Draw an altitude from point C to line AB. 2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.
3. angle CBD and angle CDA are right angles. 3. Definition of altitude
4. angel BCA angle BDC 4. All right angles are congruent.
5. angle B angle B 5. Reflexive Property
6. 6. AA Similarity Postulate
7. a/x=c/a 7.
8. a2=cx 8.
9. angle CDA angle BCA 9.
10. angle A angle A 10. Reflexive Property
11. 11. AA Similarity Postulate
12. b/y = c/b 12.
13. b2=cy 13.
14. a2+b2=cx+cy 14.
15. 15. Distributive Property
16. x+y=c 16.
17. a2+b2=c2 17.
