Chapter 12: Basics of Geometry 159
DEFINITION
The midpoint of a line segment is a point on the segment that divides it into two seg-
ments of equal length.
A segment bisector is a line, ray, or segment that divides a segment into two congruent
segments.
An angle bisector is a line, ray, or segment that passes through the vertex of an angle
and cuts it into two angles of equal size.
CHECK POINT
- M is the midpoint of segment PQ. If PM = 3 cm, MQ = __ cm and
PQ = __ cm.
- H is the midpoint of XY. If XY = 28 inches, then XH = __ inches.
- Ray AB bisects CAT. If mCAT = 86r, then mHAT = __.
- If mAXB = 27r and mBXC = 27r, then __ bisects AXC.
- mPYQ = 13r, mQY R = 12r, mRYS = 5r, and mSYT = 20r. True or False:
YR bisects PY T.
Parallel and Perpendicular Lines
Perpendicular lines are lines that intersect at right angles. The symbol
for “is perpendicular to” is ', so you can write XY AB to say that
segment XY is perpendicular to line AB. If a line, ray, or segment is
perpendicular to another segment and also divides that segment into
two congruent parts, that line, ray, or segment is the perpendicular
bisector of the segment.
When two lines are perpendicular, all the angles at the intersection
will be right angles. When two lines intersect, the vertical angles are
congruent, and the adjacent angles are linear pairs, so if one of the
angles is a right angle, all four will be right angles.
Perpendicular lines intersect to form right angles, but what about
lines that don’t intersect? Lines in the same plane that are always the
same distance apart and therefore never intersect are called parallel
lines. You see parallel lines all the time: the edges of windows and
doors, the lines on a sheet of notebook paper, and railroad tracks are
all parallel.
