Given:
ABC is a right triangle, with a right angle at ∠C
Prove:
a^2 + b^2 = c^2
Image:
https://prnt.sc/i58fyf
| Statement | Reason |
|---|---|
| 1. ABC is a right triangle, with a right angle | 1. Given |
| 2. Draw an altitude from point C to AB. | 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 | All right angles are congruent. |
| 5. ∠B ≅ ∠B | XXX |
| 6. XXX | AA Similarity Postulate |
| 7. a/x = c/a | XXX |
| 8. a^2 = cx | XXX |
| 9. ∠CDA ≅ ∠BCA | XXX |
| 10. ∠A ≅ ∠A | XXX |
| 11. XXX | AA Similarity Postulate |
| 12. b/y = c/b = | XXX |
| 13. b^2 = cy | XXX |
| 14. a^2 + b^2 = cx + cy | XXX |
| 15. XXX | Distributive Property |
| 16. x+y=c | XXX |
| 17. a^2 + b^2 = c^2 | XXX |
