Question

δxyz was reflected to form δlmn. which statements are true regarding the diagram? check all that apply. δxyz ≅ δlmn ∠y ≅ ∠m ∠x ≅ ∠l ∠z ≅ ∠l yz ≅ ml xz ≅ ln

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid - motions preserve congruence. So, if $\triangle XYZ$ is reflected to form $\triangle LMN$, then $\triangle XYZ\cong\triangle LMN$.

Step2: Identify corresponding angles

In congruent triangles, corresponding angles are congruent. $\angle X$ corresponds to $\angle L$, $\angle Y$ corresponds to $\angle M$, and $\angle Z$ corresponds to $\angle N$. So, $\angle Y\cong\angle M$ and $\angle X\cong\angle L$.

Step3: Identify corresponding sides

In congruent triangles, corresponding sides are congruent. $\overline{XZ}$ corresponds to $\overline{LN}$, $\overline{YZ}$ corresponds to $\overline{MN}$, and $\overline{XY}$ corresponds to $\overline{LM}$. So, $\overline{XZ}\cong\overline{LN}$.

Answer:

$\triangle XYZ\cong\triangle LMN$, $\angle Y\cong\angle M$, $\angle X\cong\angle L$, $\overline{XZ}\cong\overline{LN}$