Construct a perpendicular to a line l through a point A on it.
Answers
Answer:
Step-by-step explanation:
Given: point P on a given line
Construct: a line through P perpendicular to given line.
perppic
STEPS:
1. Place your compass point on P and swing an arc of any size below the line that crosses the line twice. You will be drawing at least a semicircle. (Note: While you can draw this arc above or below the line, below the arc keeps the construction lines from bumping into one another.)
2. Stretch the compass LARGER!
3. Place the compass point where the arc crossed the line on one side and make a small arc above the line (the arc could be below the line if you prefer).
4. Without changing the span on the compass, place the compass point where the first arc crossed the line on the OTHER side and make another arc. Your two small arcs should be intersecting.
5. Using a straightedge, connect the intersection of the two small arcs to point P.
perppic2
Does this construction
look familiar?
perppic2N2
dividerdash
Proof of Construction: This construction is actually another version of the construction of BISECT AN ANGLE. This construction bisected the straight angle P. Since a straight angle contains 180º, this construction created two 90º angles. Since two right angles have been formed, a perpendicular was created.
Perpendicular from a point OFF a line.
Given: point P off a given line
Construct: a line through P perpendicular to given line.
perppic
STEPS:
1. Place your compass point on P and swing an arc of any size that crosses the line twice.
2. Place the compass point on one of the two locations where the arc crossed the line and make a small arc below the line (on the side where P is not located).
3. Without changing the span on the compass, place the compass point on the other location where the first arc crossed the line and make another small arc below the line. The two small arcs should be intersecting (on the side of the line opposite of point P).
4. Using a straightedge, connect the intersection of the two small arcs to point P.
perppic2
Does this construction
look familiar?
perppic2N2
The construction method shown above on the right can also be applied to the construction where P is located ON the line.
dividerdash
Proof of Construction: Label the construction: A and B are the points of intersection with the first arc, C is the intersection of the two smaller arcs, and D is the intersection of the perpendicular with the given line. Draw pp6.
PA = PB and AC = BC since they were constructed as radii of the same circles. These segments are also congruent. Using pcas a common side, ΔPBC is congruent to ΔPAC by SSS. By CPCTC, ∠APC is congruent to ∠BPC. Now, ΔAPD is congruent to ΔBPD by SAS, with common side pd. By CPCTC, ∠PDA is congruent to ∠PDB. These two angles form a linear pair making them supplementary. If two angles are both congruent and supplementary, they are right angles. Consequently, perp8.
- make a line of any cm (more than 4.5cm)
- take your rounder(compass) place it on the left corner point
- adjust your rounder more than half of the line
- now with the same measurement make the arc above the line
- now with the same measurement place your rounder on the right point of the line and then make another arc (crossing the first arc)
do the same steps below the line with the same measurement as above.
note: pls see the image above
