Question

which of the following are valid names for the given triangle? check all that apply. a. △lmz b. △lcm c. △mlz d. △lmd e. △zml f. △zmc

Explanation:

Step1: Recall triangle - naming rule

A triangle can be named using the three vertices of the triangle in any order.

Step2: Check each option

• Option A: $\triangle LMZ$ uses the vertices $L$, $M$, and $Z$ of the given triangle, so it is a valid name.
• Option B: $\triangle LCM$ uses points $L$, $C$, and $M$. But $C$ is not a vertex of the main triangle, so it is not a valid name.
• Option C: $\triangle MLZ$ uses the vertices $M$, $L$, and $Z$ of the given triangle, so it is a valid name.
• Option D: $\triangle LMD$ uses points $L$, $M$, and $D$. But $D$ is not a vertex of the main triangle, so it is not a valid name.
• Option E: $\triangle ZML$ uses the vertices $Z$, $M$, and $L$ of the given triangle, so it is a valid name.
• Option F: $\triangle ZMC$ uses points $Z$, $M$, and $C$. But $C$ is not a vertex of the main triangle, so it is not a valid name.

Answer:

A. $\triangle LMZ$, C. $\triangle MLZ$, E. $\triangle ZML$