Question

which of the following are valid names for the triangle below? check all that apply.
a. △rm
b. △rmo
c. △mode
d. △dmr
e. △mrd
f. △sem

Explanation:

Step1: Recall triangle - naming rule

A triangle is named by its three vertices. The order of the vertices does not matter.

Step2: Identify vertices of the given triangle

The vertices of the given triangle are \(D\), \(M\), and \(R\).

Step3: Check each option

• Option A: \(\triangle RM\) has only two vertices, so it is not a valid name for a triangle.
• Option B: \(\triangle RMO\) has a non - existent vertex \(O\) (not a vertex of the given triangle), so it is not valid.
• Option C: \(\triangle MODE\) has non - existent vertices \(O\) and \(E\) (not vertices of the given triangle), so it is not valid.
• Option D: \(\triangle DMR\) uses the three vertices \(D\), \(M\), and \(R\) of the given triangle, so it is valid.
• Option E: \(\triangle MRD\) uses the three vertices \(M\), \(R\), and \(D\) of the given triangle, so it is valid.
• Option F: \(\triangle SEM\) has non - existent vertex \(S\) (not a vertex of the given triangle), so it is not valid.

Answer:

D. \(\triangle DMR\), E. \(\triangle MRD\)