Constructing Perpendicular and Parallel Lines

Constructing Perpendicular and Parallel LinesAdapted from Walch Education

Perpendicular Lines and BisectorsPerpendicular lines are two lines that intersect at a right angle (90).A perpendicular line can be constructed through the midpoint of a segment. This line is called the perpendicular bisector of the line segment.It is possible to construct a perpendicular line through a point on the given line as well as through a point not on a given line.

1.2.3: Constructing Perpendicular and Parallel Lines2

1.2.3: Constructing Perpendicular and Parallel Lines3Constructing a Perpendicular Bisector of a Line Segment Using a CompassTo construct a perpendicular bisector of , put the sharp point of your compass on endpoint A. Open the compass wider than half the distance of .Make a large arc intersecting .Without changing your compass setting, put the sharp point of the compass on endpoint B. Make a second large arc. It is important that the arcs intersect each other.(continued)

Use your straightedge to connect the points of intersection of the arcs.Label the new line .

Do not erase any of your markings. is perpendicular to line .

1.2.3: Constructing Perpendicular and Parallel Lines4Constructing a Perpendicular Bisector of a Line Segment Using Patty PaperUse a straightedge to construct onto patty paper.Fold the patty paper so point A meets point B. Be sure to crease the paper.Unfold the patty paper.Use your straightedge to mark the creased line.Label the new line .

is perpendicular to line .

1.2.3: Constructing Perpendicular and Parallel Lines5Constructing a Perpendicular Line Through a Point on the Given Line Using a CompassTo construct a perpendicular line through the point, A, on a line, put the sharp point of your compass on point A. The opening of the compass does not matter, but try to choose a setting that isnt so large or so small that its difficult to make markings.Make an arc on either side of point A on the line. Label the points of intersection C and D.Place the sharp point of the compass on point C. Open the compass so it extends beyond point A.(continued)1.2.3: Constructing Perpendicular and Parallel Lines6Create an arc on either side of the line.Without changing your compass setting, put the sharp point of the compass on endpoint D. Make a large arc on either side of the line. It is important that the arcs intersect each other.Use your straightedge to connect the points of intersection of the arcs.Label the new line .

Do not erase any of your markings. is perpendicular to line through point A.

1.2.3: Constructing Perpendicular and Parallel Lines7Constructing a Perpendicular Line Through a Point on the Given Line Using Patty PaperUse a straightedge to construct a line, , on the patty paper. Label a point on the line A.Fold the patty paper so the line folds onto itself through point A. Be sure to crease the paper.Unfold the patty paper.Use your straightedge to mark the creased line.Label the new line .

Line is perpendicular to line through point A.

1.2.3: Constructing Perpendicular and Parallel Lines8Constructing a Perpendicular Line Through a Point Not on the Given Line Using a CompassTo construct a perpendicular line through the point, G, not on the given line , put the sharp point of your compass on point G. Open the compass until it extends farther than the given line.Make a large arc that intersects the given line in exactly two places. Label the points of intersection C and D.(continued)

1.2.3: Constructing Perpendicular and Parallel Lines9Without changing your compass setting, put the sharp point of the compass on point C. Make a second arc below the given line.Without changing your compass setting, put the sharp point of the compass on point D. Make a third arc below the given line. The third arc must intersect the second arc.Label the point of intersection E.Use your straightedge to connect points G and E. Label the new line .Do not erase any of your markings.Line is perpendicular to line through point G.

1.2.3: Constructing Perpendicular and Parallel Lines10Constructing a Perpendicular Line Through a Point Not on the Given Line Using Patty PaperUse a straightedge to construct a line, , on the patty paper. Label a point not on the line, G.Fold the patty paper so the line folds onto itself through point G. Be sure to crease the paper.Unfold the patty paper.Use your straightedge to mark the creased line.Label the new line .

Line is perpendicular to line through point G.

Parallel LinesParallel lines are lines that either do not share any points and never intersect, or share all points.Any two points on one parallel line are equidistant from the other line. There are many ways to construct parallel lines.One method is to construct two lines that are both perpendicular to the same given line.1.2.3: Constructing Perpendicular and Parallel Lines11

1.2.3: Constructing Perpendicular and Parallel Lines12Constructing a Parallel Line Using a CompassTo construct a parallel line through a point, A, not on the given line , first construct a line perpendicular to .Put the sharp point of your compass on point A. Open the compass until it extends farther than lineMake a large arc that intersects the given line in exactly two places. Label the points of intersection C and D.

(continued)

1.2.3: Constructing Perpendicular and Parallel Lines13Without changing your compass setting, put the sharp point of the compass on point C. Make a second arc below the given line.Without changing your compass setting, put the sharp point of the compass on point D. Make a third arc below the given line. The third arc must intersect the second arc.Label the point of intersection E.Use your straightedge to connect points A and E. Label the new line . Line is perpendicular to line .(continued)

1.2.3: Constructing Perpendicular and Parallel Lines14Construct a second line perpendicular to line .Put the sharp point of your compass on point A. Open the compass until it extends farther than line

Make a large arc that intersects line in exactly two places. Label the points of intersection F and G.Without changing your compass setting, put the sharp point of the compass on point F. Make a second arc to the right of line .(continued)

1.2.3: Constructing Perpendicular and Parallel Lines15Without changing your compass setting, put the sharp point of the compass on point G. Make a third arc to the right of line . The third arc must intersect the second arc.Label the point of intersection H.Use your straightedge to connect points A and H. Label the new line .

Do not erase any of your markings.Line is perpendicular to line .Line is parallel to line .

1.2.3: Constructing Perpendicular and Parallel Lines16Constructing a Parallel Line Using Patty PaperUse a straightedge to construct line on the patty paper. Label a point not on the line A.Fold the patty paper so the line folds onto itself through point A. Be sure to crease the paper.Unfold the patty paper.Fold the new line onto itself through point A.Unfold the patty paper.Use your straightedge to mark the second creased line.Label the new line .Line is parallel to line .

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