Let's start with examining the given statement, the statement that we want to prove and the figure.
Given: AB=DC
Prove: AC=DB
We will write a two-column proof. In our first step, we will state the given statement.
Given
AB=DC
Next, we will use the Addition Property of Equality to add BC to both sides of the equation.
Addition Property of Equality
AB+ BC=DC+ BC
Knowing that the length from B to C is equal to the length from C to B, we can rewrite BC as CB.
Properties of Line Segments
AB+BC=DC+CB
Finally, we will add the terms by the Segment Addition Postulate to complete our proof.
Segment Addition Postulate
AC=DB
Combining these steps, let's form our two-column proof.
