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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!!!!!!!!

KennedyPape  Jan 24, 2018
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7.   a/x = c/a     ~     Corresponding parts of similar triangles are proportional

 

11.   ΔCBA ~ ΔDCA     ~     AA Similarity Postulate

 

12.   b/y = c/b    ~     Corresponding parts of similar triangles are proportional

 

15.   a^2 + b^2  =  c(x + y)     ~     Distributive Property

 

I think that is it.....

hectictar  Jan 24, 2018

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