Basic Constructions

1
Basic Constructions

• Copy a segment
• Copy an angle

2
What is a Construction?

• Uses TWO instruments only
• Compass
• Straightedge
• Since a compass measures the radius of a circle,
  and radii of a circle are congruent, then we can
  use it to construct congruent segments.
• A straightedge is used to connect two points. A
  ruler may not be used to measure distances in
  constructions.

3
What is a Construction?

• Definition
• An arc is any part of a circle.

• When we draw using a compass we will be drawing
  arcs. We rarely need to complete the entire
  circle. The radii will still be congruent even
  if a complete circle is not present.

4
Construction 1 Copy a Segment
Step 1 Use the straightedge to draw a line and
label it l
Step 2 Choose any point on l and label it C.
Step 3 Set the compass at A and make an arc at
B.
Step 4 Using the same opening, set your compass
at C and make an identical arc so that it
intersects line l. Label this point D.
5
Construction 2 Copy an Angle
Step 1 You need to start with a line l and a
point F which corresponds to C.
E
Step 2 Opening your compass to any comfortable
distance, set the compass at C and make an arc
that intersects both sides of the angle. Label
these points E and D.
D
Step 3 Using the same opening, set the compass
at F and make an identical arc which intersects
the line l. Label this point G.
Step 4 On the original angle, set the compass
at D and make an arc that intersects the other
side of the angle at E.
G
6
Construction 2 Copy an Angle
Step 5 Using the same opening, set your compass
at G and make an identical arc so that it
intersects the arc from step 3. Label this point
H.
H