Given that ADB and CDB are right angles, and BD bisects B , prove that D is the midpoint of AC . The figure shows triangle A B C. Point D lies on side A C. 1.ADB and CDB are right angles (given)2. BD bisects B (given)3. ADBCDB (Right Thm.)4. DBADBC (Def. of bisector)5. DABDCB (Interior Thm.)6. ABDCBD (AAA, Steps 3, 4, 5)7. ADDC (CPCTC)8. AD=DC (Def of )9. D is midpoint of AC (definition of midpt) 1.ADB and CDB are right angles (given)2. BD bisects B (given)3. ADBCDB (Right Thm.)4. DBADBC (Def. of bisector)5. ABCB ( Bisector Thm.)6. ABDCBD (ASA, Steps 3, 4, 5)7. ADDC (CPCTC)8. AD=DC (Def of )9. D is midpoint of AC (definition of midpt) 1.ADB and CDB are right angles (given)2. BD bisects B (given)3. ADBCDB (Right Thm.)4. BDDB (Reflex. Prop. of )5. DBADBC (Def. of bisector)6. ABDCBD (ASA, Steps 3, 4, 5)7. ADDC (CPCTC)8. AD=DC (Def of )9. D is midpoint of AC (definition of midpt) 1.ADB and CDB are right angles (given)2. BD bisects B (given)3. ADBCDB (Right Thm.)4. BDDB (Reflex. Prop. of )5. ADDC (Def. of bisector)6. ABDCBD (SAS, Steps 3, 4, 5)7. AD=DC(CPCTC)8. D is midpoint of AC (definition of midpt)

A D B C