Section 3.6- Constructing Parallel and Perpendicular
Lines
Essential Question: How can we construct parallel and perpendicular lines using
a compass and a straightedge?
Do Now:
Construction #1- Constructing Parallel Lines
Use the steps below to help you with example 1.
Given: Point D not on
Construct:
Step 1 Draw
parallel to
.
Step 2 With the compass tip on B, draw an arc that
intersects
between B and D. Label this
intersection point F. Continue the arc to intersect
at point G.
Step 3 Without changing the compass setting, place the
compass tip on D and draw an arc that intersects
above B and D. Label this intersection point H.
Step 4 Place the compass tip on F and open or close the
compass so it reaches G. Draw a short arc at G.
Step 5 Without changing the compass setting, place the
compass tip on H and draw an arc that intersects the
first arc drawn from H. Label this intersection point
J.
Step 6 Draw
, which is the required line parallel to
.
Example 1: Constructing Parallel Lines
Construct line m so it is parallel to line l.
Why must the lines be parallel? (Think about the kind of angles that are formed!)
Construction #2- Perpendicular at a Point on a Line
Objective: Construct the perpendicular to a given line at a given point on the line.
Steps:
Given: 𝒑𝒐𝒊𝒏𝒕 𝑷 𝒐𝒏 𝒍𝒊𝒏𝒆 𝒍
1. Construct two points on line 𝑙 that are
equidistant from P. Label the points A and
B.
2. Open the compass wider so the opening
1
is greater than 2 𝐴𝐵. With the compass tip
on A, draw an arc above point P.
3. With the same compass setting, place
the compass point on point B. Draw an arc
that intersects the arc from Step 2. Label
the point of intersection as C.
4. Draw ⃡𝐶𝑃
Result:
__________ ⊥ __________
Construction #3: Perpendicular from a Point to a Line
Objective: Construct the perpendicular to a given line through a given point not on the
line.
Steps:
Given: 𝒍𝒊𝒏𝒆 𝒍 𝒂𝒏𝒅 𝒑𝒐𝒊𝒏𝒕 𝒁 𝒏𝒐𝒕 𝒐𝒏 𝒍
1. Open your compass to a size greater
⃡
Objective: Construct ⃡𝒁𝑩 ⊥ 𝑪𝑿
than the distance from Z to 𝑙. Use that
setting and place the compass point on
point Z, draw an arc that intersects 𝑙 at
two points.
2. Label the points of intersection as C and
X.
3. Place your compass point on C and
make an arc below line l.
4. With the same compass setting, put the
compass tip on X and draw an arc that
intersects the arc from step 3. Label the
point of intersection as B.
4. Draw ⃡𝑍𝐵 .
Result:
__________ ⊥ __________