Question

with the information given below, can you conclude that δlmn ≅ δxyz? 32° 32° yes no

Explanation:

Step1: Identify congruent parts

In $\triangle LMN$ and $\triangle XYZ$, we have:

• Side $LN$ and $XZ$: One mark (so they are congruent, $LN = XZ$).
• Side $MN$ and $YZ$: Two marks (so they are congruent, $MN = YZ$).
• Angle $\angle N$ and $\angle Z$: Both are $32^\circ$ (so $\angle N=\angle Z$).

Step2: Apply SAS congruence criterion

The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In $\triangle LMN$ and $\triangle XYZ$, we have two sides ($LN = XZ$, $MN = YZ$) and the included angle ($\angle N=\angle Z$) congruent. So by SAS, $\triangle LMN\cong\triangle XYZ$.

Answer:

Yes