Transcript 1.5 Basic Constructions

1.6: Basic Constructions
Construction - when you use a straight edge and compass
to draw a geometric figure.
Straight Edge - a ruler with no markings
Compass - a geometric tool used to draw circles and parts
of a circle called arcs.
Constructing  Segments
(Copy a Segment )
Given: AB
Construct: CD so that CD  AB
B
1. Draw ray longer than AB
with endpoint C.
2. Place compass point at A,
mark arc at B.
3. With same compass
setting, make new arc from C
to D. Label points.
A
C
D
Constructing  s
(Copy an Angle)
Given: A
Construct: S so that S  A.
1. Draw ray with endpoint S.
B
A
2. Make arc from vertex of A
through both rays, marking pts.
of intersection B and C.
3. Use same compass setting
for S vertex to mark new
S
arc. Label intersection R.
4. Measure opening from C to
B and mark with arc.
5. Using same setting,
measure from R to find T.
C
T
R
Perpendicular Lines - 2 lines that intersect to form right
angles ( )
t
l
tl
Perpendicular Bisector of a segment is a line, segment,
or ray that is  to the segment at its midpoint thereby
bisecting the segment into 2  segments.
A
B
b
Line b bisects AB
Constructing the  Bisector
Given: AB
Construct: XY so that XY is the 
bisector of AB.
1. Place compass on A
(must be > than ½ AB).
Make arc above and
below AB near center.
2. Place compass on B. With
same setting, intersect the 2
arcs.
3. Draw  bisector XY.
X
A
B
Y
Constructing the Angle Bisector
Given: A
Construct: AD, the bisector of A.
B
1. With compass pt. at A,
construct arc through both A
rays. Mark intersection pts.
B and C. Extend compass.
2. With compass pt. at C,
draw arc. With compass pt.
at B and same setting, draw
arc making sure 2 arcs
intersect. Label pt. D.
3. Draw AD, the  bisector.
D
C
Lesson Check:
Turn to page 46 in your textbook. Complete the
Lesson check #1-6. When you’ve finished,
check your answers in the back of your book
(found on p. 898).
DO NOT WRITE IN YOUR TEXTBOOK!!!