3.7 Constructing Parallel and Perpendicular Lines

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

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

Constructing Parallel Lines http://www.mathopenref.com/constparallel.html

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.

Perpendicular at a point on a line http://www.mathopenref.com/constperplinepoint.html

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.

Perpendicular from a point to a line http://www.mathopenref.com/constperpextpoint.html

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.