Question

example 4:
a. name the intersection of abce and fdba:
b. name the intersection of aef and abce:
c. name the two planes that intersect at the line ec:
d. name the intersection of line ab and line ae:
e. name the intersection of line bc and line fc:
f. name the intersection of aef and dbc:
g. go back to the drawing above, and lightly shade plane abdf.
h. how many planes are shown in the drawing, above?

Explanation:

Step1: Recall plane - line intersection property

The intersection of two planes is a line. For the intersection of planes ABCE and FDBA, we look for the common line. Points A and B are common to both planes, so the intersection is line AB.

Step2: Analyze intersection of AEF and ABCE

The common line between plane AEF and plane ABCE is line AE as points A and E lie on both planes.

Step3: Identify planes intersecting at EC

Planes ABCE and FDEC share the line EC.

Step4: Determine intersection of two lines

The intersection of line AB and line AE is point A as it is the common point to both lines.

Step5: Find intersection of BC and FC

The intersection of line BC and line FC is point C.

Step6: Consider intersection of AEF and DBC

These two planes are parallel and have no intersection (empty - set $\varnothing$).

Step7: Shading instruction

(This is a manual task and cannot be done in text. But conceptually, shade the four - sided region with vertices A, B, D, F).

Step8: Count planes

The planes shown are ABCE, FDBA, AEF, DBC, FDEC, ABDF, so there are 6 planes.

Answer:

a. Line AB
b. Line AE
c. Planes ABCE and FDEC
d. Point A
e. Point C
f. $\varnothing$
g. (Manual shading task)
h. 6