Transcript Constructions

December 16, 2011
1) Grab a Computation Challenge, keep
it face down and put your name on
the back.
2) Write your homework in your agenda:
Review notes on constructions and
continue to study vocabulary.
3) Take out your angle pair relationship
worksheet.
4) Sharpen your pencils. Get ready for
LOTS of notes.
Angle Pair Relationship
1) Linear pair
3) Adjacent
5) Vertical
7) Linear pair
9) 1300
11) 550
13) 1450
15) 230
17) 900
19) x = 23
21) x = 20
2) Adjacent
4) Complementary
6) Adjacent
8) Vertical
10) 430
12) 270
14) 610
16) 1310
18) 730
20) x = 59
22) x = 8
What am I learning today?
Constructions
What will I do to show that I
learned it?
Perform basic constructions using both
a compass and straightedge.
QUESTION
How do I
construct line
segments?
http://www.mathopenref.com/constcopysegment.html
Constructing Line
Segments
1) Draw a line segment and label it AB
A
B
2) Draw a Ray PS so it’s longer than AB
A
P
B
S
Constructing Line
Segments
3) Draw an arc through point B on line segment
AB.
A
P
B
S
Constructing Line
Segments
4) Keep the same setting on the
compass. Draw an arc that intersects
PS at a new point Q.
A
P
B
Q
S
QUESTION
How do I construct
congruent angles?
http://www.mathopenref.com/constcopyangle.html
Constructing Congruent
Angles
1) Draw an angle and label it PQR
P
Q
R
Constructing Congruent
Angles
2) Draw a Ray ST.
P
Q
R
S
T
Constructing Congruent
Angles
3) Place the compass at vertex Q. Use a small
setting on the compass. Draw an arc that
intersects both sides of PQR to make points
X and Y.
Q
X
Y
P
R
Constructing Congruent
Angles
4) Keeping the same setting and place on point S.
Draw an arc that intersects ST. Label the
intersection Point A.
X
P
Y
R
Q
S
A
T
Constructing Congruent
Angles
5) Set the compass to measure the distance from point X to
point Y. Keeping that setting, draw an arc that intersects
the existing arc. Label that intersection Point M.
P
X
Q
M
S
Y
A
R
T
MST  PQR
MST  PQR
Constructing Congruent
Angles
6) Draw a Ray SM.
M
S
T
MST  PQR
QUESTION
How do I bisect line
segments?
http://www.mathopenref.com/constbisectline.html
Bisecting Line Segments
1) Draw a line segment CD.
C
D
Bisecting Line Segments
2) Set the compass so that it is more
than halfway to D. Draw an arc
“above” and “below” CD.
C
D
Bisecting Line Segments
3) Keeping the same setting on the compass,
place the compass on point D and draw
another arc “above” and another “below”.
The intersections create two new points Q
and R.
Q
C
D
R
Bisecting Line Segments
4) Draw a line segment by connecting
points Q and R. This will intersect CD
at a new Point M. This is the bisector
for CD.
Q
M
C
D
R
CM  MD
QUESTION
How do I bisect
angles?
http://www.mathopenref.com/constbisectangle.html
Bisecting Angles
1) Draw an angle and label it Angle ABC.
A
B
C
Bisecting Angles
2) Draw an arc that intersects both sides
of the angle. Label the points of
intersection X and Y.
A
X
B
Y
C
Bisecting Angles
3) Place the compass at point X and set
it more than halfway to Y. Draw an
arc in the interior of Angle ABC.
A
X
B
Y
C
Bisecting Angles
4) Keep that same setting and place the
compass at point at Y. Draw an arc
that intersects the arc you just drew.
Label the intersection T.
A
X
T
B
Y
C
Bisecting Angles
5) Draw a Ray BT. This is the bisector of
Angle ABC.
A
X
T
B
Y
C
December 16, 2011
1) Grab a Computation Challenge, keep
it face down and put your name on
the back.
2) Write your homework in your agenda:
Review notes on constructions and
continue to study vocabulary.
3) Sharpen your pencils. Get ready for
LOTS of notes.
QUESTION
How are parallel lines
created using a compass?
http://www.mathopenref.com/constparallel.html
Constructing Parallel
Lines
1) Draw a line and label it AB.
A
B
Constructing Parallel
Lines
2) Draw a ray at an angle with its
endpoint on the line. Label a
point R on the ray.
R
A
B
Constructing Parallel
Lines
3) Set the compass about halfway
between the endpoint of the
ray and point R. Make an arc
that intersects both the line
and ray.
Constructing Parallel
Lines
R
A
B
Constructing Parallel
Lines
4) Keep the same compass setting.
Move the compass to point R.
Draw an arc.
Constructing Parallel
Lines
R
A
B
Constructing Parallel
Lines
5) Use the compass to measure
the width of the first arc. Keep
the same setting and make
another arc from the
intersection the upper arc and
intersect it.
Constructing Parallel
Lines
R
A
B
Constructing Parallel
Lines
6) Draw a line through point R
and the intersection created by
the two upper arcs.
Constructing Parallel
Lines
R
A
B
QUESTION
How are perpendicular
lines created using a point
on the line?
http://www.mathopenref.com/constperplinepoint.html
Constructing Perpendicular
Lines with a Point on the Line
1) Draw a line. Label a point A
on the line.
A
Constructing
Perpendicular Lines
2) From point A on the line, draw an
arc to the right and the left of
point A.
A
Constructing
Perpendicular Lines
3) Set the compass on the left
intersection and extend it
between point A and right
intersection. Draw an arc above
the line.
Constructing
Perpendicular Lines
A
Constructing
Perpendicular Lines
4) Keeping the same setting, do the
same from the right intersection.
5) Draw a line through point A and
the intersection of the two arcs.
Constructing
Perpendicular Lines
A
QUESTION
How are perpendicular
lines created using a point
in space?
Constructing Perpendicular
Lines with a Point in Space
1) Draw a line AB. Label a point
X in space above the line.
X
A
B
Constructing
Perpendicular Lines
2) Draw an arc from point X that crosses
line AB in two places. Label these
points D and E. X
D
A
E
B
Constructing
Perpendicular Lines
3) Set the compass on point D and
extend it more than halfway to point
E. Draw an arc below the line.
X
D
A
E
B
Constructing
Perpendicular Lines
4) Keeping the same compass setting, set the
compass on point E. Draw another arc
below the line that intersects the first arc.
X
D
A
E
B
Constructing
Perpendicular Lines
5) Draw a line through point X and the
intersections of the two arcs.
X
D
A
E
B