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Complete the proof of the Pythagorean theorem.
Given: ΔABC is a right triangle, with a right angle at ∠C.
Prove: a^2 + b^2 = c^2
Statement: ~ Reason:
1. ΔABC is a right triangle, with a right angle at ∠C. ~ Given
2. Draw an altitude from point C to (line segment) AB ~ From a point not on a line, exactly one perpendicular can be draw through the point to the line.
3. ∠CDB and ∠CDA are right angles ~ Definition of altitude
4. ∠BCA ≅ ∠BDC ~ All right angles are congruent
5. ∠B ≅ ∠B ~ Reflexive Property
6. ΔCBA ~ ΔDBC ~ AA Similarity Postulate
7. a/x = c/a ~ Polygon Similarity Postulate
8. a^2 = cx ~ Cross Multiply and Simplify
9. ∠CDA ≅ ∠BCA ~ All Right Angles are Congruent
10. ∠A ≅ ∠A ~ Reflexive Property
11. ΔCBA ~ ΔDBA ~ AA Similarity Postulate
12. b/y = c/b = ~ Polygon Similarity Postulate
13. b^2 = cy ~ Cross Multiply and Simplify
14. a^2 + b^2 = cx +cy ~ Addition Property of Equality
15. (CB)^2 + (CA)^2 = (AB)(DB + BA) ~ Distributive Property
16. x + y = c ~ Segment Addition Postulate
17. a^2 + b^2 = c^2 ~ Substitution Property
***Everything in Bold is my answers. Please check them and help me because I dont think I did very well but Im horriable with two column proofs so PLEASE HELP ME!!!***
Thank You!!!!!!!!
