CK-12 Geometry - Second Edition

9.4. Inscribed Angles http://www.ck12.org

24.m^6 EBO

25.m^6 EOB

26.mBĈ

27.m^6 ABO

28.m^6 A

29.m^6 EDC

30. Fill in the blanks of one proof of the Inscribed Angle Theorem.

Given: Inscribed^6 ABCand diameterBDProve:m^6 ABC=^12 mAĈ

TABLE9.2:

Statement Reason

1. Inscribed^6 ABCand diameterBD
   m^6 ABE=x◦andm^6 CBE=y◦
   2.x◦+y◦=m^6 ABC


2. All radii are congruent


3. Definition of an isosceles triangle
   5.m^6 EAB=x◦andm^6 ECB=y◦
   6.m^6 AED= 2 x◦andm^6 CED= 2 y◦
   7.mAD̂= 2 x◦andmDĈ= 2 y◦


4. Arc Addition Postulate
   9.mAĈ= 2 x◦+ 2 y◦


5. Distributive PoE
   11.mAĈ= 2 m^6 ABC
   12.m^6 ABC=^12 mAĈ
   31. Use the diagram below to write a proof of Theorem 9-8.