Question

use the given information to prove that ab = cd. given: ac = bd prove: ab = cd

Explanation:

Step1: Express lengths in terms of segments

We know that $AC = AB + BC$ and $BD=BC + CD$ since a line - segment is the sum of its sub - segments.

Step2: Substitute into the given equation

Given $AC = BD$, substituting the expressions from Step 1 gives $AB + BC=BC + CD$.

Step3: Use the subtraction property of equality

Subtract $BC$ from both sides of the equation $AB + BC=BC + CD$. We get $AB+BC - BC=BC + CD - BC$.

Step4: Simplify the equation

On the left - hand side, $BC - BC = 0$, and on the right - hand side, $BC - BC = 0$. So, $AB = CD$.

Answer:

$AB = CD$