Section 1
Parallel Lines and Planes
Draw and label two parallel lines, $\ell$ and $m$. Indicate that the lines are parallel by using the arrowhead symbol.
Describe a real-world example or model of parallel lines.
Writing Math Sketch the diagram shown below. Then describe and explain the relationship between lines $\ell$ and $m$.
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{K N}, \overline{H L}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{J M}, \overline{M L}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{J M}, \overline{K H}$
Name the parts of the cube shown at the right.all planes parallel to plane $W X Q$
Name the parts of the cube shown at the right.all segments parallel to $\overline{P Q}$
Name the parts of the cube shown at the right.all segments skew to $\overline{P S}$
Name the parts of the cube shown at the right.all pairs of parallel planes
Carpentry A carpenter is constructing a chair like the one shown at the left. Describe a pair of parts that are parallel, a pair that intersect, and a pair that are skew.
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{B E}, \overline{C F}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A D}, \overline{B E}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A D}, \overline{E F}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{B C}, \overline{E F}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A B}, \overline{D E}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A B}, \overline{C F}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A B}, \overline{B C}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{A D}, \overline{B C}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{B E}, \overline{B C}$
Describe each pair of segments in the prism as parallel, skew, or intersecting.$\overline{B C}, \overline{D E}$
Name the parts of the cube shown at the right.six planes
Name the parts of the cube shown at the right.all segments parallel to $\overline{E H}$
Name the parts of the cube shown at the right.all segments skew to $\overline{G H}$
Name the parts of the cube shown at the right.all segments parallel to $\overline{A E}$
Name the parts of the cube shown at the right.all segments skew to $\overline{B F}$
Name the parts of the pyramid shown at the right.all pairs of intersecting planes
Name the parts of the pyramid shown at the right.all pairs of parallel segments
Name the parts of the pyramid shown at the right.all pairs of skew segments
Name the parts of the pyramid shown at the right.all sets of three segments that intersect in a common point
Draw and label a figure to illustrate each pair.congruent parallel segments
Draw and label a figure to illustrate each pair.parallel segments not congruent
Draw and label a figure to illustrate each pair.segments not parallel or congruent
Draw and label a figure to illustrate each pair.skew segments
Draw and label a figure to illustrate each pair.segments not intersecting or skew
Draw and label a figure to illustrate each pair.parallel planes
Draw and label a figure to illustrate each pair.intersecting planes
Draw and label a figure to illustrate each pair.parallel rays
Complete each sentence with sometimes, always, or never.Skew lines ____ intersect.
Complete each sentence with sometimes, always, or never.Skew lines are ____ parallel.
Complete each sentence with sometimes, always, or never.Two parallel lines ____ lie in the same plane.
Complete each sentence with sometimes, always, or never.Two lines in parallel planes are ____ skew.
Complete each sentence with sometimes, always, or never.Two lines that have no points in common are ___ parallel.
Complete each sentence with sometimes, always, or never.If two lines are parallel, then they ____ lie in the same plane.
Interior Design The shower stall shown in the diagram is formed by a series of intersecting planes. Name two skew segments in the diagram.
Construction The Empire State Building, built in 1930-1931, is 102 stories and reaches a height of 1250 feet. Suppose the stories represent parallel planes equal distances apart. What is the approximate distance between floors?
Sports Describe how skis on a skier's feet could intersect, be parallel, or be skew.
Graphic Arts The comic artist has used parallel lines two ways in the B.C. comic below. Explain the two uses of parallel lines in the comic.
Critical Thinking Plane $A$ is parallel to plane $B$, and plane $B$ is parallel to plane $C$. Is Plane $A$ parallel to Plane $C$ ? Write yes or no, and explain your answer. Then describe something in your school building that illustrates your response.
In the figure at the right, $\overline{B E} \perp \overline{A D}$. (Lesson 3-7)a. Name four right angles.b. Name a pair of supplementary angles.c. Name two pairs of angles whose sum is $90 .$
If $\angle J K L \cong \angle P Q R, m \angle P Q R=4 x+5$, and $m \angle J K L=5 x-12$, what is $m \angle P Q R$ ?
Refer to the figure at the right.If $m \angle C A E=78$ and $m \angle D A E=30$, find $m \angle 1$.
Refer to the figure at the right.Find $m \angle D A F$ if $m \angle D A E=30$ and $m \angle E A F=75$.
Refer to the figure at the right.Time Do the hands of a clock at 12:20 P.M. form an acute, obtuse, or right angle?
Cartography On a map of Ohio, Cincinnati is located at $(3,5)$, and Massillon is located at $(17,19)$. IfColumbus is halfway between the two cities, what ordered pair describes its position?
It is $4.5$ blocks from Carlos' house to Matt's house. From Matt's house to Keisha's house is $10.5$ blocks, and from Keisha's house to Carlos' house is 6 blocks. If they live on the same street, whose house is between the other two?
Short Response Name all the planes that can contain three of the points $J, K, L$, and $M$, if no three points are collinear and the points do not all lie in the same plane.
Multiple Choice12 is what percent of 40 ?(A) $0.3 \%$(B) $3 \frac{1}{3} \%$(C) $30 \%$(D) $33 \%$