Thursday, July 12, 2007

Geometry Chapter 1.5 Segment and Angle Bisectors

I) Vocabulary:

A) Midpoint: A midpoint of a segment is the point that divides, or bisects, the segment into two congruent segments.

B) Segment Bisector: is a segment, ray, line, or plane that intersects a segment at its midpoint.

Example: Given segment AB bisects segment CD at point E. If CD = 10, what does AE and EB equal?
10/2 = 5 so they both equal 5 units.

C) Angle Bisector: is a ray that divides an angle into two adjacent angles that are congruent.

Example: Given angle PQR is bisected by ray QS, and measure of angle SQR = 22 degrees, what is the measure of angle PQR and angle PQS?

22 x 2 = 44 so measure of angle PQR = 44 degrees and when an angle is bisected, the two angles formed are congruent so angle SQR = angle PQS = 22 degrees.

D) Midpoint Formula: the mean, or average, of the x-coordinates and the y-coordinates.

therefore the midpoint formula is: ((x1+ x2) /2, (y1+ y2) /2)
example: Given A(-1, 7) and B(3, -3) what is their midpoint?

((-1 + 3)/2, (7 + -3)/2) = (2/2, 4/2) = (1, 2)