1. 3.7 Constructing Parallel and Perpendicular Lines

2. Learning Target
I can construct parallel and perpendicular lines using a compass and a straightedge

3. Recall From Chapter 1 the constructions we have already learned.
Duplicating an angle
Duplicating a line segment
Bisecting an angle
Perpendicular Bisector

4. Constructing Parallel Lines

5. On your paper, Draw a line with with point R above it.
STEP 1: Draw a line through point R and the line at an angle to create point S.
STEP 2: With the compass on point S, draw an arc that intersects both lines.
STEP 3: With the same compass setting, do it again from point R.
STEP 4: Set the compass width the lower arc and then move it to the upper arc.
STEP 5: Mark off a point that intersects the upper arc. Call this point T.
STEP 6: Draw a straight line through S and T.

6. Perpendicular at a point on a line

7. On your paper, draw a line, and somewhere on that line put point D
STEP 1: Put your compass on point D and draw arcs on both sides that intersect the line. Name these points E and F.
STEP 2: With the compass on E, set the compass at halfway between D and F.
STEP 3: Draw an Arc above the line. Repeat from point F with the same compass setting so the arcs intersect.
STEP 4: Draw a line from point D to the point where the arcs intersect.

8. Perpendicular from a point to a line

9. On your paper draw a line, and somewhere above that line, put point A
STEP 1: Place the compass on point A and extend the compass past the line.
STEP 2: Draw two arcs across the line, name the points B and C.
STEP 3: From points A and B, draw arcs below the line so they intersect.
STEP 4: Connect point A with the point of intersection.