1. Constructions

2. Don’t change your radius!
Construction #1
Construct a segment congruent to a given segment.
This is our compass.
Given: A B
Procedure:
1. Use a straightedge to draw a line. Call it l.
Construct: XY = AB
2. Choose any point on l and label it X.
3. Set your compass for radius AB and make a mark on the line where B lies. Then, move your compass to line l and set your pointer on X. Make a mark on the line and label it Y. l X Y
Don’t change your radius!

3. Construct an angle congruent to a given angle
Construction #2
Construct an angle congruent to a given angle A C B
Given:
Procedure: D
1) Draw a ray. Label it RY.
2) Using B as center and any radius, draw an arc intersecting BA and BC. Label the points of intersection D and E. E
Construct:
3) Using R as center and the SAME RADIUS as in Step 2, draw an arc intersecting RY. Label point E2 the point where the arc intersects RY D2 R Y
4) Measure the arc from D to E. E2
5) Move the pointer to E2 and make an arc that that intersects the blue arc to get point D2
6) Draw a ray from R through D2

4. Bisector of a given angle?
Construction #3
How do I construct a
Bisector of a given angle? C A B Z
Given: X Y
Procedure:
Using B as center and any radius, draw
and arc that intersects BA at X and BC at point Y.
2. Using X as center and a suitable radius, draw an arc.
Using Y as center and the same radius, draw an arc
that intersects the arc with center X at point Z.
3. Draw BZ.

5. How do I construct a perpendicular bisector to a given segment?
Construction #4
How do I construct a perpendicular
bisector to a given segment? X
Given: A B Y
Procedure:
Using any radius greater than 1/2 AB, draw four arcs of
equal radii, two with center A and two with center B.
Label the points of intersection X and Y.
Draw XY

6. Construction #5 How do I construct a perpendicular bisector
to a given segment at a given point? Z
Given: C k X Y
Procedure:
Using C as center and any radius, draw arcs intersecting
k at X and Y.
Using X as center and any radius greater than CX, draw an arc. Using Y as center and the same radius,
draw and arc intersecting the arc with center X at Z.
Draw CZ.

7. Construction #6 How do I construct a perpendicular bisector to a
given segment at a given point outside the line? k P
Given: X Y Z
Procedure:
Using P as center, draw two arcs of equal radii that
intersect k at points X and Y.
Using X and Y as centers and a suitable radius, draw arcs
that intersect at a point Z.
Draw PZ.

8. Construction #7 How do I construct a line parallel to a
given line through a given point? k P 1 l
Given: A B
Procedure:
Let A and B be two points on line k. Draw PA.
At P, construct <1 so that <1 and <PAB are congruent
corresponding angles. Let l be the line containing the
ray you just constructed.