SAT Question 7a11ceea: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. In the figure, it’s given that segment $AD$ is perpendicular to line $l$ at point $A$. Statement I is that segment $AD$ is perpendicular to line $m$ at point $D$. It follows that angles $BAC$ and $EDC$ are right angles. Therefore, triangles $ABC$ and $DEC$ are right triangles. At least one pair of congruent corresponding sides is needed to determine triangle congruence by the side-angle-side (SAS) condition or the angle-side-angle (ASA) condition, so statement I is not sufficient to determine that triangle $ABC$ is congruent to triangle $DEC$. Statement II is that $AC=13$ and $DC=13$. It follows that triangles $ABC$ and $DEC$ share one pair of congruent corresponding sides. Two additional pairs of congruent corresponding parts are needed to determine triangle congruence by SAS condition, ASA condition, or side-side-side (SSS) condition, so statement II is not sufficient to determine that triangle $ABC$ is congruent to triangle $DEC$. Therefore, neither I nor II is sufficient by itself to determine that triangle $ABC$ is congruent to triangle $DEC$.