Question

a) how many points appear in the figure? ________
b) how many lines appear in the figure? ________
c) how many planes appear in the figure? ________
d) name three collinear points. ________
e) name four coplanar points. ________
f) name the intersection of planes abc and abe. ________
g) name the intersection of planes bch and def. ________
h) name the intersection of ad and df. ________

Explanation:

Step1: Count points

Count all distinct points in the figure. There are 8 points: A, B, C, D, E, F, G, H.

Step2: Count lines

Lines are straight - paths connecting points. Lines are: AB, BC, CD, DA, AE, BF, CG, DH, EF, FG, GH, HE. There are 12 lines.

Step3: Count planes

Planes are flat surfaces. Planes are: ABCD, EFGH, ABFE, BCGF, CDHG, DAEH. There are 6 planes.

Step4: Find collinear points

Collinear points lie on the same line. For example, A, B, C are not collinear. But A, B and the point where the line segment AB lies are collinear. Three collinear points: A, B, C (assuming they are on a straight - line segment in the figure).

Step5: Find four - coplanar points

Coplanar points lie on the same plane. For example, A, B, C, D are coplanar as they lie on the plane ABCD.

Step6: Find intersection of planes ABC and ABE

The intersection of two planes is a line. The intersection of planes ABC and ABE is line AB.

Step7: Find intersection of planes BCH and DEF

These two planes are parallel in a typical 3 - D figure like this, so the intersection is the empty set $\varnothing$.

Step8: Find intersection of AD and DF

The intersection of two line - segments is a point. The intersection of $\overline{AD}$ and $\overline{DF}$ is point D.

Answer:

a) 8
b) 12
c) 6
d) A, B, C (answers may vary)
e) A, B, C, D (answers may vary)
f) AB
g) $\varnothing$
h) D