Question

if $overline{ab}congoverline{bc}$, $ad = 4t - 51$, and $cd = t$, what is the value of $t$?

Explanation:

Step1: Apply property of congruent segments

Since $\overline{AB}\cong\overline{BC}$ and the line from $B$ is perpendicular to $AC$, by the property of the perpendicular - bisector of a segment (a line that is perpendicular to a segment and bisects it), we know that $AD = CD$.

Step2: Set up the equation

Set up the equation $4t - 51=t$.

Step3: Solve the equation for $t$

Subtract $t$ from both sides: $4t - t-51=t - t$, which simplifies to $3t-51 = 0$. Then add 51 to both sides: $3t-51 + 51=0 + 51$, getting $3t=51$. Divide both sides by 3: $\frac{3t}{3}=\frac{51}{3}$, so $t = 17$.

Answer:

$17$