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 overline{yz} ≅ overline{ml} overline{xz} ≅ overline{ln}

Explanation:

Step1: Properties of Reflection

A reflection is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, \(\triangle XYZ\cong\triangle LMN\) (by the definition of a rigid transformation).

Step2: Corresponding Angles

When two triangles are congruent (\(\triangle XYZ\cong\triangle LMN\)), their corresponding angles are congruent.

• \(\angle X\) corresponds to \(\angle L\), so \(\angle X\cong\angle L\)
• \(\angle Y\) corresponds to \(\angle M\), so \(\angle Y\cong\angle M\)
• \(\angle Z\) corresponds to \(\angle N\), not \(\angle L\)

Step3: Corresponding Sides

When two triangles are congruent (\(\triangle XYZ\cong\triangle LMN\)), their corresponding sides are congruent.

• \(YZ\) corresponds to \(MN\), not \(ML\)
• \(XZ\) corresponds to \(LN\), so \(XZ\cong LN\)

Answer:

\(\triangle XYZ\cong\triangle LMN\), \(\angle Y\cong\angle M\), \(\angle X\cong\angle L\), \(XZ\cong LN\)