Question

given the prism shown to the right, name the following
a. vertices
b. edges
c. faces
d. intersection of face bcq and edge $overline{qr}$
e. intersection of face bcq and face odr
e. determine the intersection of face bcq and face odr. choose the correct answer below

Explanation:

Step1: Identify vertices

Vertices are corner - points. The vertices of the prism are B, C, Q, O, D, R.

Step2: Identify edges

Edges are line - segments where two faces meet. The edges are $\overline{BC}$, $\overline{CQ}$, $\overline{BQ}$, $\overline{OD}$, $\overline{DR}$, $\overline{OR}$, $\overline{BO}$, $\overline{CD}$, $\overline{QR}$.

Step3: Identify faces

Faces are flat surfaces. The faces are face BCQ, face ODR, face BODC, face BQR O, face CDRQ.

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

The point where edge $\overline{QR}$ intersects face BCQ is point Q.

Step5: Find intersection of face BCQ and face ODR

The two faces BCQ and ODR are parallel, so the intersection is $\varnothing$.

Answer:

a. B, C, Q, O, D, R
b. $\overline{BC}$, $\overline{CQ}$, $\overline{BQ}$, $\overline{OD}$, $\overline{DR}$, $\overline{OR}$, $\overline{BO}$, $\overline{CD}$, $\overline{QR}$
c. face BCQ, face ODR, face BODC, face BQR O, face CDRQ
d. Q
e. The intersection is $\varnothing$