Question

Complete the equations and reasons to show that AC = EC.

BC = DC, AB = ED
A) AC = Segment Addition Postulate
B) AC = ED + DC Substitution Property of Equality
C) ED + DC = Segment Addition Postulate
D) AC= Transitive Property of Equality"

Answer 1

To show that AC = EC and BC = DC, we use the segment addition postulate and substitution property of equality. We first write AC = AB + BC, then substitute AB with ED and BC with DC. Next, we reverse the equation and write AC = EC. This is supported by the transitive property of equality.

Step-by-step explanation:

To show that AC = EC and BC = DC, we can use the segment addition postulate and the substitution property of equality. Here are the steps:

1. AC = AB + BC (Segment Addition Postulate)
2. AC = ED + DC (Substitution Property of Equality, since AB = ED and BC = DC)
3. ED + DC = AC (Segment Addition Postulate, reversing the equation)
4. AC = EC (Transitive Property of Equality, since AC = AC)