Perpendicular Bisectors
Define Perpendicular Bisector
A line that cuts a segment in half at a right angle.
Define angle bisectors
A line that splits an angle into two equal parts.
What is a line that divides a segment into two equal parts at a right angle called?
A perpendicular bisector.
n triangle ABC, angle bisector AD splits BC into segments of lengths 3 and 6. Find the ratio of AB to AC.
AB:AC = 3:6 = 1:2.
How do you find the slope of a perpendicular bisector in a coordinate plane?
Take the negative reciprocal of the slope of the original segment.
Triangle sides are AB = 8, AC = 6. Use the Angle Bisector Theorem to find BD:DC.
BD:DC = AB:AC = 8:6 = 4:3.
The point where all perpendicular bisectors of a triangle intersect is called the
Circumcenter
Triangle sides are AB = 8, AC = 6. Use the Angle Bisector Theorem to find BD:DC.
BD:DC = AB:AC = 8:6 = 4:3.
A segment has endpoints (2,3) and (6,7). Find the equation of the perpendicular bisector.
Midpoint = (4,5), slope = 1 → perpendicular slope = -1 → equation: y - 5 = -1(x - 4) → y = -x + 9.
Triangle ABC has vertices A(0,0), B(4,0), and C(0,6). An angle bisector is drawn from A to side BC. Find the coordinates of the point D where the angle bisector intersects BC.
Answer: = (3,3)