Download 8.5b (build)—Constructing Parallel Lines

(8-4) CONSTRUCTIONS: Parallel Lines & Polygons in Circles
8.5b (build)—Constructing Parallel Lines
Name: ________________________
Used (build)—Constructing
with permission from Math Open
Reference
8.5b
Parallel
Lines
http://www.mathopenref.com/constparallel.html
Used with permission from Math Open Reference
Constructing parallel lines
http://www.mathopenref.com/constparallel.html
Step 1: Draw a line through R that intersects the line PQ at any angle, forming the point J where it intersects
Constructing parallel lines
the line PQ .
Step
1:
Draw
a line
throughwidth
R that
the line
angle, R
forming
the point
J where
PQ at any
Step 2: With the
compass
setintersects
to about half
the distance
between
and J, place
the point
on itJ, intersects
and draw
the
line
.
PQ
an arc across both lines RJ and PQ .
Step 2: With the compass width set to about half the distance between R and J, place the point on J, and draw
Step 3: Without adjusting the compass width, move the compass to R and draw a similar arc to the one in
an
arc2.across both lines RJ and PQ .
step
Step
4:
Set
compass
widththe
to compass
the distance
between
the lower
crosses
two lines
point
Step 3: Without
adjusting
width,
movewhere
the compass
to arc
R and
drawthe
a similar
arc (one
to theend
oneatin
T and
step
2. the other at point K). Move the compass to where the upper arc crosses the line RJ (at point X)
andcompass
draw an width
arc across
thedistance
upper arc,
forming
point
Step 4: Set
to the
between
where
theS.lower arc crosses the two lines (one end at point
Step 5: TDraw
a
straight
line
through
points
R
and
S.
and the other at point K). Move the compass to where the upper arc crosses the line RJ (at point X)
draw
anline
arc across
the upper
arc,line
forming
RS is parallel
to the
Step 6: and
Done.
The
PQ . point S.
Step 5: Draw a straight line through points R and S.




Step 6: Done. The line RS is parallel to the line PQ .
A. Practice constructing parallel lines.
1.
2.
A. Practice constructing parallel lines.
1.
2.
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120
3.
4.
B. Do the constructions below. Use a compass and straight-edge or computer software. Explain the
construction processes.
5. Construct a line parallel to the one below that
1.
passes through the point R.
6.
2.
7. Construct a line parallel to the one below that
passes through the point R.
Construct a line parallel to AB through T, and
another line parallel to CD also through T. What
do you know about the resulting shape?
8. Construct a line parallel to the one below that
passes through the point R.
R
R
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8.5c (apply)—Constructing Polygons Inscribed in Circles
Used with permission from Math Open Reference
http://www.mathopenref.com/constequilateral.html
Constructing an equilateral triangle in a circle
Start: Start with the line segment AB, which is the length of the sides of the
desired equilateral triangle.
Step 1: Pick a point P that will be one vertex of the finished triangle.
Step 2: Place the point of the compass on the point A and set it's drawing end
to point B. The compass is now set to the length of the sides of the
finished triangle. Do not change it from now on.
Step 3: With the compass point on P, make two arcs, each roughly where the
other two vertices of the triangle will be.
Step 4: On one of the arcs, mark a point Q that will be a second vertex of the
triangle. It does not matter which arc you pick, or where on the arc
you draw the point.
Step 5: Place the compass point on Q and draw an arc that crosses the other
arc, creating point R.
Done:
The ∆PQR is an equilateral triangle. Its side length is equal to the
distance AB.
Used with permission from Math Open Reference
http://www.mathopenref.com/constinhexagon.html
Construct a hexagon in a circle
Start: Start with a given circle, center O.
A
Step 1: Mark a point anywhere on the circle and label it A. This will be the first vertex
of the hexagon.
Step 2: Set the compass on this point and set the width of the compass to the center of
the circle. The compass is now set to the radius of the circle.
Step 3: Make an arc across the circle. This will be the next vertex of the hexagon.
Step 4: Move the compass on to the next vertex and draw another arc. This is the third
vertex of the hexagon.
Step 5: Continue in this way until you have all six vertices.
Step 6: Draw a line between each successive pairs of vertices, for a total of six lines.
Done:
These lines form a regular hexagon inscribed in the given circle.
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O
1.
9. Create a circle. Use compass and straightedge to find the center.
2. Construct an equilateral triangle inscribed in a circle. Be prepared to explain why the
10.
construction works. (Use what you know about triangles, circles, copying and bisecting segments and
angles, and creating parallel and perpendicular lines.)
a. With a compass and straight-edge.
b. Using computer software.
3. Construct a hexagon inscribed in a given circle with compass and straightedge. Be prepared to
11.
explain why the construction works. (Use what you know about hexagons, circles, copying and
bisecting segments and angles, and creating parallel and perpendicular lines.)
a. With a compass and straight-edge.
b. Using computer software.
4. Construct a square inscribed in a circle. Be prepared to explain why the construction works. (Use
12.
what you know about squares, circles, copying and bisecting segments and angles, and creating parallel
and perpendicular lines.)
a. With a compass and straight-edge.
b. Using computer software.
Extra Challenge Task: Construct a pentagon inscribed in a circle. Be prepared to explain why the
construction works. (Use what you know about pentagons, circles, copying and bisecting segments and
angles, and creating parallel and perpendicular lines.)
a. With a compass and straight-edge.
b. Using computer software.
8.5d (apply)—Review Constructions
REVIEW:
Use the line segments below to construct the following.
1. 3CD
2. AB + EF
3. 2AB + CD
4. 2CD – 3AB
5. Mr. Anderson is making four corner tables for his classroom. He has one large square piece of wood that he
plans to make the four tabletops from. He begins my marking the needed cuts for the tabletops on the
square piece of wood.
a. Bisect one angle of the square. Extend the angle bisector so that it
now intersects the square in two places. Where does the bisector
intersect the square?
b. Bisect the remaining angles of the square piece of wood. Mr.
AndersonSec
cuts
along each angle bisector he created. What figures
Math 1 In-Sync by Jordan School District, Utah is licensed under a
did he
create?
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Commons Attribution-NonCommercial-ShareAlike 3.0 United States License
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6. Nate would like to create a basketball court on the rectangular patio behind his house.