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

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

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

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.

Practice: A B

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.

APractice: 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

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.

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

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