1. 1.6 Basic Constructions SOL: G4 Objectives: The Student Will …
Construct congruent segments.
Construct congruent angles.
Construct perpendicular bisectors and angle bisectors.

2. Straightedge Compass Construction A ruler with no markings on it.
A geometric tool used to draw circles and parts of circles called arcs.
Construction
A geometric figure drawn using a straightedge and a compass

3. Example 1: Construct Congruent Segments
Given: AB
Construct: CD so that CD  AB A B
1st Step: Draw a ray with endpoint C C
2nd Step: Open the compass to the
length of AB
3rd Step: with the same compass setting
put the compass point on point C.
Draw an arc that intersects the ray.
Label the point of intersection D.

4. Example 2: Construct Congruent Angles
Given: ∡A
Construct: ∡S so that ∡S  ∡A
1st Step: Draw a ray with endpoint S
2nd Step: With the compass point on vertex A, draw an arc that
intersects the sides of ∡A. Label the points of intersection
B and C. S

5. Example 2: Construct Congruent Angles
Given: ∡A
Construct: ∡S so that ∡S  ∡A
3rd Step: With the same compass setting
put the compass point on point S. Draw
an arc and label it point of intersection with that intersects
the ray as R.
4th Step: Open the compass to the length BC. Keeping the
same compass setting, put the compass point on R.
Draw an arc to locate T.
5th Step: Draw ST. S

6. Perpendicular Bisector
Perpendicular Lines ⊥
Two lines that intersect to form right angles
Perpendicular Bisector
A line, segment, or ray that is perpendicular to the segment at its midpoint

7. Example 3: Construct the Perpendicular Bisector
Given: AB
Construct: XY so that XY is the perpendicular bisector of AB
1st Step: Put the compass point on
point A and draw a long arc. Make
sure the compass is open passed
the ½ mark of AB. A B
2nd Step: With the same compass setting,
put the compass point on point B and draw
another long arc. Label the points where
the two arcs intersect X and Y.
3rd Step: Connect points X and Y. Label the midpoint of XY and
AB as point M.

8. Example 2: Construct Angle Bisector
Given: ∡A
Construct: AD, the bisector of ∡A
1st Step: Put the compass on vertex A. Draw an arc that
intersects the sides of ∡A. Label the points of intersection B and C.
2nd Step: Put the compass point on point C and draw an arc. With the
same compass setting, draw an arc using point B. Be sure the arcs
intersect. Label the point where the two arcs intersect D.
3rd Step: Draw AD. AD is the bisector of ∡A.