Statements
1. bis the midpoint of ac
2. ab = bc
3. ab = cd
4. ab = cd
5. bc=cd
6. c is the midpoint of bd

Step-by-step explanation:

Given: B is the midpoint of AC;

segment AB is congruent to segment CD;

Prove: BC = 1/2*BD

B is the midpoint of AC : given;

AB = BC : definition of midpoint

AB is congruent to CD : given;

AB = CD : definition of congruent segments;

BC = CD : substitution/transitive;

BC + CD = BD : property of line segment addition

BC + BC = BD : substitution

2*BC = BD : combining like terms

BC = 1/2*BD : division property of equality

C is the midpoint of BD : definition of midpoint as C is halfway between B and D

answer: the first graph

step-by-step explanation: