Question

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 $overleftrightarrow{pq}$ and $overleftrightarrow{mo}$. ____________
h) name the intersection of plane k and line c. ____________
i) give another name for plane l. ____________
j) give another name for $overleftrightarrow{pq}$. ____________

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: Count points in first diagram

Count all distinct labeled points. There are 9 points ($P, S, T, M, N, O, U, R, Q$).

Step2: Count lines in first diagram

Identify straight - line paths. There are 5 lines ($\overleftrightarrow{PQ}$, $\overleftrightarrow{MO}$, $\overleftrightarrow{RS}$, $\overleftrightarrow{d}$, $\overleftrightarrow{e}$).

Step3: Count planes in first diagram

Identify flat surfaces. There are 2 planes ($K$ and $L$).

Step4: Name collinear points in first diagram

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

Step5: Name non - coplanar points in first diagram

Points not on the same plane. $P, T, U, R$ are non - coplanar.

Step6: Rename line $e$ in first diagram

$\overleftrightarrow{MN}$ is another name for line $e$.

Step7: Find intersection of $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MO}$ in first diagram

The intersection point is $N$.

Step8: Find intersection of plane $K$ and line $c$ in first diagram

The intersection point is $R$.

Step9: Rename plane $L$ in first diagram

Plane $MNO$ is another name for plane $L$.

Step10: Rename $\overleftrightarrow{PQ}$ in first diagram

$\overleftrightarrow{NQ}$ is another name for $\overleftrightarrow{PQ}$.

Step11: Count points in second diagram

Count all distinct labeled points. There are 8 points ($A, B, C, D, E, F, G, H$).

Step12: Count lines in second diagram

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: Count planes in second diagram

Identify flat surfaces. There are 6 planes ($ABC$, $ABE$, $BCD$, $DEF$, $BCH$, $ADFG$).

Step14: Name collinear points in second diagram

Points on the same straight line. $A, E, F$ are collinear.

Step15: Name coplanar points in second diagram

Points on the same plane. $A, B, C, D$ are coplanar.

Step16: Find intersection of planes $ABC$ and $ABE$ in second diagram

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

Step17: Find intersection of planes $BCH$ and $DEF$ in second diagram

Since the planes are parallel, the intersection is the empty set $\varnothing$.

Step18: Find intersection of $\overline{AD}$ and $\overline{DF}$ in second diagram

The intersection point is $D$.

Answer:

2.
a) 9
b) 5
c) 2
d) $M, N, O$
e) $P, T, U, R$
f) $\overleftrightarrow{MN}$
g) $N$
h) $R$
i) Plane $MNO$
j) $\overleftrightarrow{NQ}$
3.
a) 8
b) 12
c) 6
d) $A, E, F$
e) $A, B, C, D$
f) $\overline{AB}$
g) $\varnothing$
h) $D$