1. definition of a midpoint
definition of an angle bisector

2. A B C
Given: B is midpoint of AC
Prove: AB = BC
Statement Reason
B is midpoint of AC given

3. A B C
Given: B is midpoint of AC
Prove: AB = BC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint

4. A B C
Given: B is midpoint of AC
Prove: AC = 2(BC)
Statement Reason
B is midpoint of AC given

5. A B C
Given: B is midpoint of AC
Prove: AC = 2(BC)
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint

6. A B C
Given: B is midpoint of AC
Prove: AC = 2(BC)
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate

7. A B C
Given: B is midpoint of AC
Prove: AC = 2(BC)
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution

8. A B C
Given: B is midpoint of AC
Prove: AC = 2(BC)
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution
AC = 2(BC) combine like terms

9. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given

10. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint

11. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate

12. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution

13. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution
AC = 2(BC) combine like terms

14. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution
AC = 2(BC) combine like terms
(1/2)AC = BC division property

15. A B C
Given: B is midpoint of AC
Prove: BC = (1/2)AC
Statement Reason
B is midpoint of AC given
AB = BC definition of midpoint
AC = AB + BC segment addition postulate
AC = BC + BC substitution
AC = 2(BC) combine like terms
(1/2)AC = BC division property
BC = (1/2)AC symmetric property

16. A B
Given: BD bisects <ABC
Prove: <1 = <2
<1
<2 D C
Statement Reason
BD bisects <ABC given

17. A B
Given: BD bisects <ABC
Prove: <1 = <2
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector

18. A B
Given: BD bisects <ABC
Prove: <ABC = 2(<1)
<1
<2 D C
Statement Reason
BD bisects <ABC given

19. A B
Given: BD bisects <ABC
Prove: <ABC = 2(<1)
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector

20. A B
Given: BD bisects <ABC
Prove: <ABC = 2(<1)
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate

21. A B
Given: BD bisects <ABC
Prove: <ABC = 2(<1)
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution

22. A B
Given: BD bisects <ABC
Prove: <ABC = 2(<1)
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution
<ABC = 2(<1) combine like terms

23. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given

24. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector

25. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate

26. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution

27. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution
<ABC = 2(<1) combine like terms

28. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution
<ABC = 2(<1) combine like terms
(1/2)<ABC = <1 division property

29. A B
Given: BD bisects <ABC
Prove: <1 = (1/2)<ABC
<1
<2 D C
Statement Reason
BD bisects <ABC given
<1 = <2 definition of angle bisector
<ABC = <1 + <2 angle addition postulate
<ABC = <1 + <1 substitution
<ABC = 2(<1) combine like terms
(1/2)<ABC = <1 division property
<1 = (1/2)<ABC symmetric property