SOLUTION: Using your knowledge of similarity and the relationships in a right triangle, write a two column proof of the Pythagorean Thereom from the diagram below of right triangle ABC with

Algebra ->  Geometry-proofs -> SOLUTION: Using your knowledge of similarity and the relationships in a right triangle, write a two column proof of the Pythagorean Thereom from the diagram below of right triangle ABC with       Log On


   

Question 1023230: Using your knowledge of similarity and the relationships in a right triangle, write a two column proof of the Pythagorean Thereom from the diagram below of right triangle ABC with altitude CD drawn to hypotenuse AB.
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
 


1. ΔACD∽ΔCBD∽ΔABC             1.If an altitude is drawn to the 
                               hypotenuse of a given right 
                               triangle, the two right 
                               triangles formed are similar 
                               to each other and to the given 
                               triangle.

2. AC%2F%28AB%29=AD%2F%28AC%29                   2. Corresponding parts of
                               similar triangles

3.  AC² = AD×AB                3. Product of means equal
                               product of extremes (in 2)

4. BC%2F%28AB%29=BD%2F%28BC%29                   4. Corresponding parts of
                               similar triangles

5.  BC² = BD×AB                5. Product of means equal
                               product of extremes (in 4)

6.  AC²+BC² = AD×AB+BD×AB      6. Equals added to equals
                               gives equals

7.  AC²+BC² = AB×(AD+BD)       7. Distributive property

8.  AD+BD = AB                 8. A whole equals the sum 
                               of its parts.

9.  AC²+BC² = AB×AB            9. Substitution

10. AC²+BC² = AB²             10. AB×AB = AB²

Edwin