Question

use the pyramid to complete parts (a) through (f) below.
b. what is the intersection of planes cde, abe, and abc?
a. the line through ∅ and point e
b. the line through ∅ and point c
c. ∅
d. point d
e. point e
f. point c
c. what is the intersection of \overleftrightarrow{cd} and \overleftrightarrow{de}?
a. point e
b. ∅
c. plane cde
d. point d

Explanation:

Part b

Step1: Recall plane intersection rule

Two planes intersect in a line, and three planes' intersection is the common line or point. Planes CDE, ABE, ABC: Find common line. Plane ABE and ABC share line AB? No, plane CDE: points C, D, E; ABE: A, B, E; ABC: A, B, C. Common point? Wait, no—wait, the pyramid: let's visualize. Plane CDE (C, D, E), plane ABE (A, B, E), plane ABC (A, B, C). The intersection of three planes: find the line common to all? Wait, no, maybe the intersection is the line through ∅ (maybe a typo, maybe vertex) and E? Wait, option A: The line through ∅ and Point E. Wait, maybe the pyramid has a vertex, say ∅ (maybe O or a vertex). Wait, looking at the diagram, E is a vertex. Wait, planes CDE, ABE, ABC: plane ABE and CDE: do they share line BE? No. Wait, maybe the intersection is the line through the common vertex (maybe ∅) and E. So option A: The line through ∅ and Point E.

Step2: Eliminate other options

Option B: line through ∅ and C: C is in ABC and CDE, but E is in ABE and CDE. So common line should include E. Option C: ∅ (empty set) no. Option D: Point D: D is in CDE, not in ABC. Option E: Point E: E is in ABE and CDE, but ABC? No, ABC has A, B, C. Wait, maybe the diagram shows that the intersection of three planes is the line through the apex (∅) and E. So answer A.

Part c

Step1: Recall line intersection rule

Two lines intersect at a point. Lines CD and DE: they share point D (since CD is from C to D, DE is from D to E). So their intersection is point D? Wait, options: A. Point E (E is end of DE, not CD), B. ∅ (no), C. Plane CDE (intersection of lines is a point, not plane), D. Point D (CD and DE meet at D). So check: line CD has points C, D; line DE has D, E. So intersection is D.

Answer:

(Part b): A. The line through ∅ and Point E