Points, Lines, Planes and Angles

The plane that contains the top of the box can be called plane ABCD.

Are there more than four points in plane ABCD?

The plane that contains the top of the box can be called plane ABCD.

Name the intersection of planes ABFE and BCGF.

The plane that contains the top of the box can be called plane ABCD.

Name two planes that do not intersect.

Make a sketch showing four coplanar points such that three, but not four, of them, are collinear.

Make a sketch showing four points that are not coplanar.

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Name five planes that contain sides of the pyramid shown.

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Of the five planes containing sides of the pyramid, are there any that do not intersect?

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Name three lines that intersect at point R.

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Name two planes that intersect in $\overleftrightarrow{ST}$.

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Name three planes that intersect at point S.

A plane can be named by three or more non-collinear points it contains. In chapter 12 you will study pyramids like the one shown at the right below.

Name a line and a plane that intersect in a point.

Follow the steps shown to draw the figure named.

A rectangular solid or box.

Follow the steps shown to draw the figure named.

A barn

Name two planes that intersect in $\overleftrightarrow{FG}$.

Name three lines that intersect at point E.

Name three planes that intersect at point B.

a. Are points $A$, $D$ and $C$ collinear?

b. Are points $A$, $D$ and $C$ coplanar?

a. Are points $R$, $S$, $G$ and $F$ coplanar?

b. Are points $R$, $S$, $G$ and $C$ coplanar?

a. Name two planes that do not intersect.

b. Name two other planes that do not intersect. 

You can think of the ceiling and floor or a room as parts of horizontal planes. The walls are parts of vertical planes. Vertical planes are represented by figures like those shown in which two sides are vertical. A horizontal plane is represented by a figure like that shown, with two sides horizontal and no sides vertical.

Can two horizontal planes intersect?

You can think of the ceiling and floor or a room as parts of horizontal planes. The walls are parts of vertical planes. Vertical planes are represented by figures like those shown in which two sides are vertical. A horizontal plane is represented by a figure like that shown, with two sides horizontal and no sides vertical.

a. Can two vertical planes intersect?

b. Suppose a line is known to be in a vertical plane. Does the line have to be a vertical line?

Sketch and label the figures described. Use dashes for hidden parts.

Vertical line l intersects a horizontal plane M at point O.

Sketch and label the figures described. Use dashes for hidden parts.

Horizontal plane P contains two lines k and n that intersect at point A.

Sketch and label the figures described. Use dashes for hidden parts.

The horizontal plane Q and vertical plane N intersect.

Sketch and label the figures described. Use dashes for hidden parts.

Vertical planes X and Y intersect in $\overleftrightarrow{AB}$.

Sketch and label the figures described. Use dashes for hidden parts.

Point P is not in plane N. Three lines through point P intersect N in points A, B, and C.

Sketch and label the figures described. Use dashes for hidden parts.

Three vertical planes intersect in a line.

Sketch and label the figures described. Use dashes for hidden parts.

A vertical plane intersects two horizontal planes in lines I and n.

Sketch and label the figures described. Use dashes for hidden parts.

Three planes intersect in a point.

Find the value of the variable.

Name the point that appears to satisfy the description.

Equidistant from R and S.

Find the value of the variable.

2. $8+c=13$

Name the point that appears to satisfy the description.

Equidistant from S and U.

Find the value of the variable.

$c-15=12$

Name the point that appears to satisfy the description.

Equidistant from U and T.

Find the value of the variable.

$7-z=13$

Classify each statement as true or false.

Plane Y and $\overleftrightarrow{PQ}$ intersect in a point L.

Classify each statement as true or false.

Points J, K, L, and N are coplanar.

Find the value of the variable.

$15-z=0$

Classify each statement as true or false.

Points J, L, and Q are collinear.

Find the value of the variable.

$4x=28$

Find the value of the variable.

$3x=15$

Draw a vertical plane $Z$ intersecting a horizontal $l$ line in a point $T$.

Find the value of the variable.

$7x=-35$

Find the value of the variable.

$-5x=-5$

Find the value of the variable.

$\frac{1}{3}a=2$

Find the value of the variable.

$\frac{3}{4}a=9$

Find the value of the variable.

$\frac{4}{5}a=-20$

Find the value of the variable.

$-2b=6$

Find the value of the variable.

$-3b=-9$