Question

refer to the figure for exercises 1 - 7.

1. name the lines that are only in plane q.
2. how many planes are labeled in the figure?
3. name the plane containing the lines m and l.
4. name the intersection of lines m and l.
5. name a point that is not coplanar with points a, b, and c.
6. are points f, m, g, and p coplanar? explain.
7. does line n intersect line p? explain.

example 2
name the geometric terms modeled by each object or phrase.

1. one solar panel
2. a tabletop
3. bridge support beam

Explanation:

Step1: Identify lines in plane Q

By observing the figure, we find the lines within plane Q.
Lines in plane Q are lines that have all their points in plane Q. Let's assume from the figure, lines $\overleftrightarrow{GL}$ and $\overleftrightarrow{GH}$ are only in plane Q.

Step2: Count labeled planes

We look for planes with labels. From the figure, planes $m$, $n$ and the unnamed vertical - like plane are labeled. So there are 3 labeled planes.

Step3: Name plane with lines m and l

The plane that contains lines $m$ and $l$ is plane $m$.

Step4: Find intersection of lines m and l

The intersection of two lines is the point they have in common. If lines $m$ and $l$ intersect at point $C$, then the intersection is point $C$.

Step5: Find non - coplanar point

Points $A$, $B$, and $C$ are in plane $m$. A point not in plane $m$ is non - coplanar with them. For example, point $D$ is not in plane $m$, so point $D$ is not coplanar with $A$, $B$, and $C$.

Step6: Determine coplanarity of points F, M, G, P

Points $F$ and $C$ are in plane $m$, point $M$ is between planes $m$ and $n$, point $G$ is in plane $n$ and point $P$ is on the vertical - like line. Since these points do not all lie on the same flat surface (plane), they are not coplanar.

Step7: Check line intersection

We need to see if the lines will cross. If the lines are skew (not in the same plane and do not intersect) or parallel (in the same plane and do not intersect), they do not intersect. If they are in different planes and not parallel, they may intersect. Let's assume from the figure, if line $n$ and line $l$ are in different planes and their extensions do not cross, they do not intersect.

Step8: Name geometric term for solar panel

A solar panel is flat and extends in two dimensions, so it models a plane.

Step9: Name geometric term for tabletop

A tabletop is also flat and two - dimensional, so it models a plane.

Step10: Name geometric term for bridge support beam

A bridge support beam is long and thin, and it models a line.

Answer:

1. Lines $\overleftrightarrow{GL}$, $\overleftrightarrow{GH}$ (assuming from the figure)
2. 3
3. Plane $m$
4. Point $C$ (assuming from the intersection in the figure)
5. Point $D$
6. No, they are not in the same plane.
7. No (assuming from the figure if they are skew or non - intersecting in different planes)
8. Plane
9. Plane
10. Line