Question

What is the missing statement in the proof? Scroll down to see the entire proof
Statement


Reason

1. Draw BD¯¯¯¯¯⊥AC¯¯¯¯¯ (view diagram).


construction

2. ∠ABC≅∠BDC


Angles with the same measure are congruent.

3.


Reflexive Property of Congruence

4. ΔABC~ΔBDC


AA criterion for similarity

5. BCDC=ACBC


Corresponding sides of similar triangles are proportional.

6. BC2 = AC × DC


cross multiplication

7. ∠ABC≅∠ADB


Angles with the same measure are congruent.

8. ∠BAC≅∠DAB


Reflexive Property of Congruence

9. ΔABC~ΔADB


AA criterion for similarity

10.ABAD=ACAB


Corresponding sides of similar triangles are proportional.

11. AB2 = AC × AD


cross multiplication

12. AB2 + BC2 = AC × AD + AC × DC


addition

13. AB2 + BC2 = AC(AD + DC)


Distributive Property

14. AB2 + BC2 = AC × AC


segment addition

15. AB2 + BC2 = AC2


multiplication.