Question

1. use the diagram to answer the following questions.

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 a line containing point v.
e) name the intersection of lines a and b.
f) give another name for line b.
g) name three non - collinear points.
h) give another name for plane d.
use the diagram to answer the following questions.
a) how many points appear in the figure?
b) how many lines appear in the figure?
c) how many planes appear in the figure?
name three collinear points.
name four non - coplanar points.
give another name for line e.
name the intersection of $overrightarrow{pq}$ and $overrightarrow{mo}$.
name the intersection of plane k and line c.
give another name for plane l.
give another name for $overrightarrow{pq}$.
use the diagram to answer the following questions.
how many points appear in the figure?
how many lines appear in the figure?
how many planes appear in the figure?
name three collinear points.
name four coplanar points.
name the intersection of planes abc and abe.
name the intersection of planes bch and def.
name the intersection of $overline{ad}$ and $overline{df}$.

Explanation:

Step1: Count points in first figure

By observing the first - given figure, we can directly count the number of points. There are 8 points: A, B, C, D, E, F, G, H.

Step2: Count lines in first figure

Lines are formed by connecting points. Counting all the distinct line - segments and extended lines, we find there are 12 lines.

Step3: Count planes in first figure

Planes are flat surfaces. By visual inspection, we identify 5 planes.

Step4: Find collinear points in first figure

Collinear points lie on the same straight - line. Points A, E, D are on the same line.

Step5: Find coplanar points in first figure

Coplanar points lie on the same plane. Points A, B, C, F are on the same plane.

Step6: Find intersection of planes ABC and ABE

The intersection of two planes is a line. For planes ABC and ABE, the common line is AB.

Step7: Analyze intersection of planes BCH and DEF

Since planes BCH and DEF are parallel (assuming a standard 3 - D geometric interpretation from the figure), they do not intersect, so the intersection is the empty set $\varnothing$.

Step8: Find intersection of $\overline{AD}$ and $\overline{DF}$

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

Answer:

a) 8 points
b) 12 lines
c) 5 planes
d) A, E, D
e) A, B, C, F
f) AB
g) $\varnothing$
h) D