Constructing Parallel and Perpendicular Lines

Geometry: Constructing Parallel and Perpendicular Lines

This is a free lesson from our course in Geometry


	In this lesson you�ll learn about the concepts and procedure to construct Parallel and Perpendicular Lines, using the earlier learning about the basics of compass & straightedge construction and apply them as tools to build an understanding to develop skills of higher concepts. The presentation covering such content will be done by the instructor in own handwriting, using video and with the help of several examples with solution. (More text below video...)

Other useful lessons:

Angle Bisectors and Perpendicular Bisectors

Midpoint of a Line Segment

(Continued from above) You know from earlier learning that parallel lines are coplanar lines which do not intersect and perpendicular lines are two lines that intersect to form right angles. The symbol for parallel lines is

and symbol for "perpendicular" is

. Further learn the steps now and explanation how to construct them. E.g. construct a line through a given point, parallel to a given line.

Given: line

and a point P; construct a line through the point, parallel to the given line.
Construct: a parallel line
Procedure and steps of construction:
� draw line AB, locate and mark point P (Figure 1).

� draw line through point P, intersecting line AB at M. Now you can plan to construct an angle with vertex P, congruent to the angle of intersection (Figure 2).
� center the compass at point M and draw an arc to intersect both lines. Using the same radius of the compass, center it at point P and draw another arc (Figure 3, 4).

� set the compass radius to the distance between the two intersection points of the first arc. Then center the compass at the point where the second arc intersects line PM. Mark the arc intersection point O (Figure 5). Use straight edge to join P and O and draw the line.

� Conclusion: line PO is parallel to line AB (Figure 6).
Given: Line

and a point P; construct a line through the point, perpendicular to the given line.
Construct: a line perpendicular to the given line
Procedure and steps of construction:
� draw line, containing point P (Figure 1).

� with P as center and a suitable radius draw arcs that intersect line at two points i.e. C and D (Figure 2).

� with P as center and a suitable radius draw an arcs that intersect line

at two points i.e. C and D. Using C and D as centers and with a radius of greater length than the used one before, draw arcs intersecting at Q (Figure 3,4).
� use straightedge to draw line

. Conclusion: line QP is perpendicular to line

at P (Figure 5).

Proof: You�ll notice that the construction bisects straight

APB.

APQ and

BPQ are right angles. Thus QP is perpendicular to line

, since two lines intersecting at right angles are perpendicular to each other.
The video above will explain more in detail about Constructing Parallel and Perpendicular Lines, with the help of several examples.

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