Question

question 4 of 10
which of the following are valid names for the triangle below? check all that
apply.
triangle image with vertices j, k, e (and other labeled points a, r, o)
a. △jaoe
b. △ke
c. △jke
d. △ejr
e. △kej
f. △je

Explanation:

Step1: Recall Triangle Naming Rule

A triangle is named by its three vertices, using the vertex labels. The order doesn't matter as long as all three vertices are included.

Step2: Identify Triangle Vertices

From the diagram, the vertices of the triangle are \( J \), \( K \), and \( E \).

Step3: Evaluate Each Option

• Option A (\(\triangle JAOE\)): Contains extra vertices (\(A, O\)) not part of the triangle. Invalid.
• Option B (\(\triangle KE\)): Only two vertices. A triangle needs three. Invalid.
• Option C (\(\triangle JKE\)): Includes all three vertices \( J, K, E \). Valid.
• Option D (\(\triangle EJR\)): Contains vertex \( R \) not part of the triangle. Invalid.
• Option E (\(\triangle KEJ\)): Includes all three vertices \( K, E, J \) (same as \( J, K, E \) in different order). Valid.
• Option F (\(\triangle JE\)): Only two vertices. Invalid.

Answer:

C. \(\triangle JKE\), E. \(\triangle KEJ\)