Question

1. yasmin reflects △abc over (overline{de}). she labels the reflected triangle (abc). which statement about △(abc) is not true? a. (mangle a = 76^{circ}) b. (mangle c = 43^{circ}) c. (moverline{ab}=7) d. (moverline{ac}=10)

Explanation:

Step1: Recall reflection properties

A reflection is a rigid - motion. Rigid motions preserve angle measures and side lengths.

Step2: Analyze angle measures

In a reflection of $\triangle ABC$ to $\triangle A'B'C'$ over $\overline{DE}$, $\angle A$ corresponds to $\angle A'$, $\angle B$ corresponds to $\angle B'$, and $\angle C$ corresponds to $\angle C'$. So $m\angle A'=m\angle A = 76^{\circ}$, $m\angle C'=m\angle C = 43^{\circ}$.

Step3: Analyze side - lengths

Side $\overline{AB}$ corresponds to $\overline{A'B'}$, and side $\overline{AC}$ corresponds to $\overline{A'C'}$. So $m\overline{A'B'}=m\overline{AB}=7$ and $m\overline{A'C'}=m\overline{AC}=9$, not $10$.

Answer:

D. $m\overline{A'C'}=10$