1. Aim: How do we use a compass and straightedge to perform all compass constructions?
DO NOW! – Using the given line, construct a 45 degree angle.
A B

2. Congruent Line Segments:
Draw line segment AB and an external point X.
Measure AB with compass.
Keeping the distance place the center at X and draw the same arc. Label line XY.
Practice:
A B X

3. Congruent Angles Draw line ST.
Given angle PQR put center at Q and draw an arc that intercepts both rays of the angle. Name these points X and Y.
Keeping the distance, put center on S and draw the same arc intersecting ST. Label this A.
Place compass so both tips are on X and Y and draw arc. Keeping the same distance place the steel tip at A. Draw an arc that intersects the arc you drew in the previous step. Label this point M.
Draw QM. P
Practice:
Q R

4. Perpendicular Bisector
Equilateral Triangle
Given line AB, use A as center and measure with compass. Draw arc on B.
Keeping same distance and using B as the center construct BC.
Do the same from point A
Label C where arcs intersect. Draw line segments AC and BC.
Practice:
A B
Perpendicular Bisector
Given line AB, open compass to be more than half of AB.
Using A as center, draw an arc above and below AB. Do the same using B as the center.
Draw line CD through the points where the arcs intercept.
A B

5. Angle Bisector
Given angle ABC, draw arc that intercepts both rays of the angle at points D and F.
Keeping the same distances, draw an arc from D and the F that intersect at E.
Draw BE. A
Practice:
B C
Median of Triangle
Given triangle ABC, construct RS, the perpendicular bisector of BC.
Label M where line RS intersects side BC. Draw AM.
Practice: A
B C

6. Perpendicular line to a given line through a point on the line
Given line AB with point P on the line, using P as center, draw an arc that intercepts line AB at points C and D.
Using C as the center open compass to be more than half of CD and draw arc. Do the same using D as the center and label where they meet, Point E.
Draw line EP
Practice:
A P B
-What if P is an external point? Draw diagram.

7. Parallel Line to Given Line Through External Point:
Given line AB and external point P, draw line through P intersecting AB at R that will be used as the transversal. (Let S be any point on the ray opposite PR.)
From points P and R, construct congruent corresponding angles.
Practice: P
A B

8. Group Work / Pair Share
-Given the following circle P, and AB as the diameter:
Construct the perpendicular bisector of AB to the top and bottom of circle P and label it RS where it meets the circle.
Draw triangle PRB and find the median PM.
Construct a line parallel to AB through point R. (You may extend RS.)
State the relationship between this parallel line and circle P.
A B P