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 $overleftrightarrow{pq}$ 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.
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 2nd diagram

Count distinct dots. There are 10 points: $P, S, T, M, N, O, U, R, Q, L$.

Step2: Count lines in 2nd diagram

Identify straight - line segments with arrows or double - ended arrows. There are 5 lines: $\overleftrightarrow{PQ}, \overleftrightarrow{MO}, \overleftrightarrow{e}, \overleftrightarrow{c}, \overleftrightarrow{d}$.

Step3: Count planes in 2nd diagram

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

Step4: Name collinear points in 2nd diagram

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

Step5: Name non - coplanar points in 2nd diagram

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

Step6: Rename line $e$ in 2nd diagram

It can be named $\overleftrightarrow{MN}$.

Step7: Find intersection of $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MO}$ in 2nd diagram

The intersection point is $N$.

Step8: Find intersection of plane $K$ and line $c$ in 2nd diagram

The intersection point is $R$.

Step9: Rename plane $L$ in 2nd diagram

It can be named plane $MNO$.

Step10: Rename $\overleftrightarrow{PQ}$ in 2nd diagram

It can be named $\overleftrightarrow{QP}$.

Step1: Count points in 3rd diagram

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

Step2: Count lines in 3rd diagram

Identify straight - line segments with arrows or double - ended arrows. There are 12 lines (e.g., $\overline{AB}, \overline{BC}, \overline{CD}, \overline{DA}, \overline{AE}, \overline{EF}, \overline{FH}, \overline{HE}, \overline{AD}, \overline{DF}, \overline{BE}, \overline{CH}$).

Step3: Count planes in 3rd diagram

Identify flat surfaces. There are 5 planes: plane $ABC$, plane $ABE$, plane $BCH$, plane $DEF$, plane $ADFE$.

Step4: Name collinear points in 3rd diagram

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

Step5: Name coplanar points in 3rd diagram

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

Step6: Find intersection of planes $ABC$ and $ABE$ in 3rd diagram

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

Step7: Find intersection of planes $BCH$ and $ABE$ in 3rd diagram

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

Step8: Find intersection of planes $BCH$ and $DEF$ in 3rd diagram

The intersection is a line (not named in the given points directly, but exists as the common part of the two planes).

Step9: Find intersection of $\overline{AD}$ and $\overline{DF}$ in 3rd diagram

The intersection point is $D$.

Answer:

a) 10
b) 5
c) 2
d) $M, N, O$
e) $P, T, U, R$
f) $\overleftrightarrow{MN}$
g) $N$
h) $R$
i) plane $MNO$
j) $\overleftrightarrow{QP}$

(For the 3rd set of questions about the 3rd diagram)