Final answer:
To prove that AC equals BD given AB equals CD, a two-column proof involving the Segment Addition Postulate and properties of equality and substitution is used.
Step-by-step explanation:
To prove AC = BD given that AB = CD, we will use the properties of equality and congruence in geometry in a two-column proof format. We can assume that points A, B, C, and D are distinct and lie on a straight line in this order.Two-Column ProofExplanationAnswer1. GivenAB = CD2. By the Segment Addition PostulateAB + BC = AC and CD + DB = BD3. Substitute the equality from step 1 into the equationsCD + BC = AC and AB + DB = BD4. By substitution (if segments are equal,
they can be substituted for one another)AC = BDIn a two-column proof, we start by stating the given equation ab = cd. Then, we set up two proportions by equating the ratios of the lengths and simplifying them. The final simplified ratio shows that ac = bd.By following these steps, we have shown that if two segments AB and CD are equal, then the segments that result when a third segment (BC or DB) is added to each are also equal (AC = BD).