GEOMETRY
SECTION 5.1 DAY 1 – CONSTRUCTIONS OF PERPENDICULAR BISECTORS
Target Goal: - Construct a perpendicular bisector and analyze its properties
PERPENDICULAR LINES
Constructing perpendicular lines through a given point.
1. Place your compass at P and draw an arc that intersects your line twice. Label the
intersections A and B.
2. Place your compass on A and draw an arc below the line and arc. Do the same with B. Arcs
should intersect at a point called W.
3. Use a straightedge to draw ⃡PW. ⃡PW is ⊥ to the line. Label where your line and ⃡PW intersect
D.
P
PERPENDICULAR BISECTOR
Constructing a perpendicular bisector
1. Place a compass at one of the endpoints.
3. Adjust the compass to slightly longer than half the line.
4. Draw arcs above and below the line.
5. Keeping the same compass width, draw arcs from the other endpoint.
6. Place ruler where the arcs cross and draw a line.
7. Call the point where the lines intersect M. M is the midpoint.
PERPENDICULAR BISECTOR THEOREM:
Measure the distance from C to B and from C to A
C
CA  ___________ CB  ____________
D
Measure the distance from D to B and from D to A
A
B
DA  ___________ DB  ____________
E
Measure the distance from E to B and from E to A
EA  ___________ EB  ____________
Look at the results of the measurements and look for a pattern. What do you notice?
*****Make a general statement about any point that is on a perpendicular bisector:
Notice that P and D are both equidistant from A and B.
P
Measure PKA  _______ and PKB  _______ .
Measure AK  ________and KB  ________
A
Is PD a perpendicular bisector? ________
(2,-3)
K
D
How do you know?
Make a general statement about a point that is equidistant from the endpoints of a segment.
B