Question

geometry
1.1 homework

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 $overleftrightarrow{pq}$.

Explanation:

Step1: Count points in first figure

There are 6 points ($V$, $W$, $X$, $Y$, $Z$).

Step2: Count lines in first figure

There are 2 lines ($a$ and $b$).

Step3: Count planes in first figure

There is 1 plane ($D$).

Step4: Name line with point $V$

Line $a$ contains point $V$.

Step5: Find intersection of lines $a$ and $b$

The intersection is point $W$.

Step6: Rename line $b$

Line $b$ can be named $\overleftrightarrow{WZ}$.

Step7: Name non - collinear points

$V$, $X$, $Y$ are non - collinear.

Step8: Rename plane $D$

Plane $D$ can be named plane $VWXYZ$.

Step9: Count points in second figure

There are 10 points ($M$, $N$, $O$, $P$, $Q$, $R$, $S$, $T$, $U$).

Step10: Count lines in second figure

There are 4 lines ($c$, $d$, $e$, $\overleftrightarrow{PQ}$).

Step11: Count planes in second figure

There are 2 planes ($K$ and $L$).

Step12: Name collinear points

$M$, $N$, $O$ are collinear.

Step13: Name non - coplanar points

$P$, $T$, $U$, $M$ are non - coplanar.

Step14: Rename line $e$

Line $e$ can be named $\overleftrightarrow{MO}$.

Step15: Find intersection of $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MO}$

The intersection is point $N$.

Step16: Find intersection of plane $K$ and line $c$

The intersection is point $R$.

Step17: Rename plane $L$

Plane $L$ can be named plane $MNOPU$.

Step18: Rename $\overleftrightarrow{PQ}$

$\overleftrightarrow{PQ}$ can be named $\overleftrightarrow{RN}$.

Answer:

1.
a) 6
b) 2
c) 1
d) Line $a$
e) Point $W$
f) $\overleftrightarrow{WZ}$
g) $V$, $X$, $Y$
h) Plane $VWXYZ$
2.
a) 10
b) 4
c) 2
d) $M$, $N$, $O$
e) $P$, $T$, $U$, $M$
f) $\overleftrightarrow{MO}$
g) Point $N$
h) Point $R$
i) Plane $MNOPU$
j) $\overleftrightarrow{RN}$