Question

1. find y if $overline{ad}congoverline{bc}$ and $overline{ab}=30$.

Explanation:

Step1: Understand segment - equality

Since $\overline{AD}\cong\overline{BC}$, it means the lengths of segment $AD$ and segment $BC$ are equal.

Step2: Use segment - addition postulate

We know that $AB = AD + DC+CB$. Given $AB = 30$ and $DC = 8$, and let $AD = BC=x$. Then $AB=2x + 8$.

Step3: Solve for $x$ (which is equal to $y$)

Substitute $AB = 30$ into the equation $30=2x + 8$. First, subtract 8 from both sides: $30−8=2x$, so $22 = 2x$. Then divide both sides by 2: $x=\frac{22}{2}=11$. Since $y$ represents the length of $BC$ and $BC=x$, $y = 11$.

Answer:

$11$