Question

given the prism shown to the right, name the following
a. vertices
b. edges
c. faces
d. intersection of face bcq and edge qr
e. intersection of face bcq and face odr
c. determine the faces of the prism. select all that apply

Explanation:

Step1: Identify vertices

Vertices are corner - points. Vertices are O, B, C, D, Q, R.

Step2: Identify edges

Edges are line - segments connecting vertices. Edges are $\overline{OB}$, $\overline{BC}$, $\overline{CO}$, $\overline{OD}$, $\overline{DQ}$, $\overline{QR}$, $\overline{RO}$, $\overline{BQ}$, $\overline{CD}$, $\overline{DR}$, $\overline{CQ}$.

Step3: Identify faces

Faces are flat surfaces. Faces are $\triangle OBC$, $\triangle ODR$, $\triangle BCQ$, $\triangle DQR$, quadrilateral $OBCD$, quadrilateral $OQRD$.

Step4: Find intersection of face BCQ and edge $\overline{QR}$

The intersection of face $BCQ$ and edge $\overline{QR}$ is point $Q$ since edge $\overline{QR}$ lies on face $BCQ$ and $Q$ is an endpoint of $\overline{QR}$.

Step5: Find intersection of face BCQ and face ODR

The intersection of face $BCQ$ and face $ODR$ is line - segment $\overline{DQ}$ as it is the common part of the two faces.

Answer:

a. Vertices: O, B, C, D, Q, R
b. Edges: $\overline{OB}$, $\overline{BC}$, $\overline{CO}$, $\overline{OD}$, $\overline{DQ}$, $\overline{QR}$, $\overline{RO}$, $\overline{BQ}$, $\overline{CD}$, $\overline{DR}$, $\overline{CQ}$
c. Faces: $\triangle OBC$, $\triangle ODR$, $\triangle BCQ$, $\triangle DQR$, quadrilateral $OBCD$, quadrilateral $OQRD$
d. Intersection of face $BCQ$ and edge $\overline{QR}$: Q
e. Intersection of face $BCQ$ and face $ODR$: $\overline{DQ}$