Question

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

∠BDC≅∠ADB

∠BCA≅∠DCB

∠BAC≅∠BAD

∠DBC≅∠BAC

Answer 1

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

∠BDC≅∠ADB

∠BCA≅∠DCB

∠BAC≅∠BAD

∠DBC≅∠BAC
Done
Given: ΔABC with m∠ABC = 90° (view diagram)

Prove: AB2 + BC2 = AC2

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

Answer 2

@mr.chrzanowski

Answer 3

yep he right