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 pq and mo.
h) name the intersection of plane k and line c.
i) give another name for plane l.
j) give another name for 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 ad and df.

Explanation:

Step1: Analyze figure 2 - points

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

Step2: Analyze figure 2 - lines

Count the straight - line paths. There are 5 lines: $\overleftrightarrow{MN}, \overleftrightarrow{PQ}, \overleftrightarrow{MO}, \overleftrightarrow{c}, \overleftrightarrow{d}$.

Step3: Analyze figure 2 - planes

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

Step4: Analyze figure 2 - collinear points

Points on the same straight line are collinear. $M, N, O$ are collinear.

Step5: Analyze figure 2 - non - coplanar points

Points not on the same plane. $P, S, U, M$ are non - coplanar.

Step6: Analyze figure 2 - line e

Another name for line $\overleftrightarrow{MN}$ is $\overleftrightarrow{NM}$.

Step7: Analyze figure 2 - intersection of $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MO}$

The intersection point is $N$.

Step8: Analyze figure 2 - intersection of plane $K$ and line $c$

The intersection point is $R$.

Step9: Analyze figure 2 - another name for plane $L$

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

Step10: Analyze figure 2 - another name for $\overleftrightarrow{PQ}$

Another name for $\overleftrightarrow{PQ}$ is $\overleftrightarrow{QP}$.

Step11: Analyze figure 3 - points

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

Step12: Analyze figure 3 - lines

Count the straight - line paths. There are 12 lines: $\overline{AB}, \overline{BC}, \overline{CD}, \overline{DA}, \overline{AE}, \overline{BE}, \overline{CE}, \overline{DE}, \overline{EF}, \overline{FG}, \overline{GH}, \overline{HE}$.

Step13: Analyze figure 3 - planes

Count the flat surfaces. There are 6 planes: plane $ABCD$, plane $ABEF$, plane $BCGH$, plane $DEFG$, plane $ADHE$, plane $CDHG$.

Step14: Analyze figure 3 - collinear points

$A, E, B$ are collinear.

Step15: Analyze figure 3 - coplanar points

$A, B, C, D$ are coplanar.

Step16: Analyze figure 3 - intersection of planes $ABC$ and $ABE$

The intersection is line $\overline{AB}$.

Step17: Analyze figure 3 - intersection of planes $BCH$ and $DEF$

The intersection is line $\overline{EF}$.

Step18: Analyze figure 3 - intersection of $\overline{AD}$ and $\overline{DF}$

The intersection is point $D$.

Answer:

2.
a) 8
b) 5
c) 2
d) $M, N, O$
e) $P, S, U, M$
f) $\overleftrightarrow{NM}$
g) $N$
h) $R$
i) plane $MNO$
j) $\overleftrightarrow{QP}$
3.
a) 8
b) 12
c) 6
d) $A, E, B$
e) $A, B, C, D$
f) $\overline{AB}$
g) $\overline{EF}$
h) $D$