Let's examine parallel and perpendicular lines by building a bench box. We can start by building the frame (with wooden boards).
First, we want the bottom to be a rectangle, 40 inches long and 20 inches wide.
1) To make sure the first two boards are perpendicular, let's find \(x\).
2) How many parallel boards can be placed at the end of the perpendicular initial board? What is the name of the postulate that makes this true?
3) We've labeled the boards "\(a\)", "\(b\)", and "\(c\)". Boards "\(a\)" and "\(c\)" are parallel. What is the geometric term for board "\(b\)"?
4) Boards "\(b\)" and "\(c\)" intersect at \(90^{\circ}\), what is the relationship between "b" and "c"? How many boards with this relationship can be added to board "\(b\)"? Explain your answer.
Now let's add board "\(d\)" to complete the bottom of the frame.
Now let's add board "\(d\)" to complete the bottom of the frame.
It's time to add the side boards, all \(\perp\) to the bottom frame. See boards "\(e\)", "\(f\)", "\(g\)", and "\(h\)".
5) What is the relationship between these side boards"\(e\)", "\(f\)", "\(g\)", and "\(h\)"? Explain.
6) Name a pair of boards that are "skew". (use the diagram above)
Let's complete the frame by adding the top boards. See "\(i\)", "\(j\)", "\(k\)", and "\(l\)". Use this diagram for problems 7, 8, and 9.
6) Name a pair of boards that are "skew". (use the diagram above)
Let's complete the frame by adding the top boards. See "\(i\)", "\(j\)", "\(k\)", and "\(l\)". Use this diagram for problems 7, 8, and 9.
7) Name all the boards \(\parallel\) to board "\(i\)". Use correct notation.
8) Name all the boards \(\perp\) to board "\(j\)". Use correct notation.
9) Name all three board skew with board "\(h\)".
Now, we will label the corners (vertices) and start adding the panels, starting with the bottom (which is extended and colored for easy identification). Use this diagram for problems 10, 11, and 12.
8) Name all the boards \(\perp\) to board "\(j\)". Use correct notation.
9) Name all three board skew with board "\(h\)".
Now, we will label the corners (vertices) and start adding the panels, starting with the bottom (which is extended and colored for easy identification). Use this diagram for problems 10, 11, and 12.
10) Name the plane that represents the bottom panel. Use correct notation.
11) Name the panel that will be parallel to the given bottom panel.
12) Name all four panels that will be perpendicular to the given bottom panel.
Enjoy your new bench!
11) Name the panel that will be parallel to the given bottom panel.
12) Name all four panels that will be perpendicular to the given bottom panel.
Enjoy your new bench!
Use the map of Manhattan, NY below to answer the questions.
13) What is the relationship between 42nd Street and 49th Street?
14) What is the relationship between Park Avenue and 53rd Street?
15) Name a street that is a transversal that is not perpendicular to other streets.
16) Name two streets that are perpendicular.
17) Name two streets that are parallel.
Review
18)Solve the system of equations. \(\begin{cases} 3x + 4y = 8 \\ 7x – 2y = 13 \end{cases}\)
19) Solve the system of equations. \(\begin{cases} \dfrac{1}{2}x - \dfrac{1}{4}y = 10 \\ \dfrac{1}{8}x – \dfrac{1}{8}y = 19 \end{cases}\)
20) Create two ordered pairs that have a slope of \(-\dfrac{2}{9}\)
14) What is the relationship between Park Avenue and 53rd Street?
15) Name a street that is a transversal that is not perpendicular to other streets.
16) Name two streets that are perpendicular.
17) Name two streets that are parallel.
Review
18)Solve the system of equations. \(\begin{cases} 3x + 4y = 8 \\ 7x – 2y = 13 \end{cases}\)
19) Solve the system of equations. \(\begin{cases} \dfrac{1}{2}x - \dfrac{1}{4}y = 10 \\ \dfrac{1}{8}x – \dfrac{1}{8}y = 19 \end{cases}\)
20) Create two ordered pairs that have a slope of \(-\dfrac{2}{9}\)