how do you do AB=CD and prove AC=BD

Question

AB=CD is given AND I need to prove AC=BD 1. AB=CD Given 2. BC=BC Reflexive 3. AB+BC=AC CD+BC=BD ??? 4. AB+BC=AC AB+BC=BD ??? 5. AC=BD ???

Answer 1

Yes, it sounds like the points are co-linear

AB = CD <-- given

BC = BC <--- reflexive

AB + BC = CD + BC <--- addition property of equality

AB + BC = BC + CD <--- commutative property of addition

AC = BD <-- line segment addition postulate

line segments are equal since their measures are the same