3-6 Constructing Parallel and Perpendicular Lines
Objective
SWBAT construct parallel and perpendicular lines.
Essential Info
Last lesson, we learned the Parallel Postulate, a point not on a line, there is a
unique line parallel to the given line.
Constructing Parallel Lines
Construct the line parallel to a given line and through a given point that is not on
the line.
Given: Line L and point N not on L.
Construct: Line m through N with m11L.
Step 1: Label two points H and J on the line L, draw the line connecting those two
points.
Step 2: At the point not on the line, construct and <1 congruent to <NHJ. Label
the new line m. Why must lines L an dm be parallel?
Constructing a Special Quadrilateral
Construct a quadrilateral with one pair of parallel sides of lengths a and b.
Given: Segments of lengths a = _______________, b = __________.
Construct: Quadrilateral ABYZ with AZ = a, BY = b, and AZ11BY.
Step 1: Need parallel lines, so construct parallel lines as you did in the previous
problem. Start with drawing a ray with endpoint A. Then draw ray AB with point
B not on the first ray.
Step 2: Construct corresponding angles.
Step3: Construct Y and Z so that BY = b, and AZ = a. Draw YZ.
Perpendicular at a Point on a Line
Construct the perpendicular to a given line at a given point on the line.
Given: Point P on line L.
Construct: Line CP with CP perpendicular to L.
Step 1: Construct two points on L that are equidistant from P. Label pts A and B.
Step 2: Open the compass wider so there opening is grater than 1/2 AB. With
the compass tip on A, draw an arc above point P.
Step 3: Without changing the compass setting, place the compass point on point
B. Draw an arc that intersects the arc from Step 2. Label the point of
intersection C. Draw CP.
Postulate 3-3 Perpendicular Postulate
Through a point not on a line, there is one and only one line perpendicular to the
given line. There is exactly one line through P perpendicular to L.
Perpendicular From a Point to a Line.
Construct the perpendicular to a given line through a given point not on the line.
Given: Line L and point R not on L.
Construct: Line RG with RG perpendicular to L.
Step 1: Open your compass to a size greater than the distance from R to L. With
the compass on point R, draw an arc that intersection L at two points. Label the
point E and F. Step 2: Place the compass point on E and make an arc.
Step 3: Keep the same compass setting. With the compass tip on F, draw an arc
that intersections the arc from step 2. Label the point of intersection G. Draw
line RG.
Examples
1. Draw a segment. Label its length m. Construct quadrilateral ABCD with
AB11CD, so that AB = m and CD = 2m.
2. Use a straightedge to draw EF. Construct FG so that FG is perpendicular to
EF at F.
3. Draw CX and a point A not on CX. Construct ZB so that ZB is perpendicular
to CX.
Homework
Day 1: Page 186 #7-15; Day 2: Page 187 #16-25