Question

09/03 - segment bisector practice l (updated)
possible points: 2.17
explain how you would use common segment theorem to solve for the length of segment ab given that $overline{ac}congoverline{bd}$ and point b is the mid - point of $overline{ac}$.
ab =
ac
bc
cd
ce
de

Explanation:

Step1: Use mid - point property

Since B is the mid - point of $\overline{AC}$, $AB = BC$. Given $BC = 40$, so $AB=40$.

Step2: Use congruent segments property

We are given $\overline{AC}\cong\overline{BD}$. Also, $AC=AB + BC=2x + 12+40$ and $BD=40 + 3x$. Since $AB = BC = 40$, we can also verify using the congruence. But to find $AB$, we already know from the mid - point property that $AB = 40$.

Answer:

40