SAT Question 697b3954: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. It’s given that $△ABC$ is congruent to $△BDE$. Corresponding sides of congruent triangles are equal in length. It’s given that $r$, which represents the length of $\overline{AB}$, is equal to $54$ and $s$, which represents the length of $\overline{DE}$, is equal to $26$. Since $\overline{AB}$ and $\overline{DE}$ aren’t equal in length, it follows that $\overline{AB}$ corresponds to $\overline{BD}$ and $\overline{BC}$ corresponds to $\overline{DE}$. Therefore, the length of $\overline{BD}$ is $54$ and the length of $\overline{BC}$ is $26$. The points $B$, $C$, and $D$ lie on a straight line, so the length of $\overline{BD}$ can be expressed as the sum of the lengths of $\overline{BC}$ and $\overline{CD}$. This relationship can be written as $BD=BC+CD$. Substituting $54$ for $BD$ and $26$ for $BC$ in this equation yields $54=26+CD$. Subtracting $26$ from both sides of this equation yields $CD=28$. Therefore, the length of $\overline{CD}$ is $28$.