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.

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 three collinear points.
e) name four non - coplanar points.
f) give another name for line e.
g) name the intersection of $overrightarrow{pq}$ and $overrightarrow{mo}$.
h) name the intersection of plane k and line c.
i) give another name for plane l.
j) give another name for $overrightarrow{pq}$.

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 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 $overline{ad}$ and $overline{df}$.

Explanation:

Step1: Analyze figure 2 - points

Count distinct points in the figure. There are 8 points: $M$, $N$, $O$, $P$, $Q$, $R$, $S$, $T$, $U$.

Step2: Analyze figure 2 - lines

Identify straight - line paths. There are 6 lines: $\overleftrightarrow{MN}$, $\overleftrightarrow{NO}$, $\overleftrightarrow{PQ}$, $\overleftrightarrow{RS}$, $\overleftrightarrow{MO}$, $\overleftrightarrow{c}$.

Step3: Analyze figure 2 - planes

Find flat surfaces. There are 2 planes: plane $K$ and plane $L$.

Step4: Analyze figure 2 - collinear points

Look for points on the same straight line. Three collinear points are $M$, $N$, $O$.

Step5: Analyze figure 2 - non - coplanar points

Find points not on the same plane. Four non - coplanar points could be $P$, $T$, $M$, $U$ (assuming they do not all lie on the same plane).

Step6: Analyze figure 2 - line name

Another name for line $e$ could be $\overleftrightarrow{MN}$.

Step7: Analyze figure 2 - line intersection

The intersection of $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MO}$ is point $N$.

Step8: Analyze figure 2 - plane and line intersection

The intersection of plane $K$ and line $c$ is point $R$.

Step9: Analyze figure 2 - plane name

Another name for plane $L$ could be plane $MNO$.

Step10: Analyze figure 2 - line name

Another name for $\overleftrightarrow{PQ}$ could be $\overleftrightarrow{QP}$.

Step11: Analyze figure 3 - points

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

Step12: Analyze figure 3 - lines

Identify straight - line paths. There are 12 lines: $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DA}$, $\overline{AE}$, $\overline{EF}$, $\overline{FG}$, $\overline{GH}$, $\overline{HE}$, $\overline{AC}$, $\overline{BD}$, $\overline{DF}$.

Step13: Analyze figure 3 - planes

Find flat surfaces. There are 6 planes: plane $ABC$, plane $ABE$, plane $BCH$, plane $DEF$, plane $ADFE$, plane $BCGH$.

Step14: Analyze figure 3 - collinear points

Look for points on the same straight line. Three collinear points are $A$, $E$, $D$.

Step15: Analyze figure 3 - coplanar points

Find points on the same plane. Four coplanar points are $A$, $B$, $C$, $E$ (lying on plane $ABC$ and plane $ABE$).

Step16: Analyze figure 3 - plane intersection

The intersection of planes $ABC$ and $ABE$ is line $\overline{AB}$.

Step17: Analyze figure 3 - plane intersection

The intersection of planes $BCH$ and $DEF$ is a line (not clearly named in the given notation, but it is the common line between the two planes).

Step18: Analyze figure 3 - line intersection

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

Answer:

2.
a) 8
b) 6
c) 2
d) $M$, $N$, $O$
e) $P$, $T$, $M$, $U$
f) $\overleftrightarrow{MN}$
g) $N$
h) $R$
i) plane $MNO$
j) $\overleftrightarrow{QP}$
3.
a) 8
b) 12
c) 6
d) $A$, $E$, $D$
e) $A$, $B$, $C$, $E$
f) $\overline{AB}$
g) A line (not clearly named in given notation)
h) $D$