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Guided Notes for Chapter 3
Lesson 3.2
A
is a line, ray, or segment in a plane that passes
through the midpoint of a segment in a plane.
A line that is a bisector and is perpendicular to a line segment is its
.
The segment connecting the vertex of a triangle to the midpoint of its
opposite side is a
. There are three midpoints and three
vertices in every triangle, so every triangle has three
.
The segment that connects the midpoints of two sides of a triangle is a
. A triangle has three sides, each side with its own
midpoint, so there are three
in every triangle.
Lesson 3.3
The shortest distance from a point to a line is measured along the
from the point to the line.
The
from a
to a
segment from the point to the line.
is the length of the perpendicular
An
of a triangle is a perpendicular segment from a vertex to the
opposite side or to a line containing the opposite side.
Lesson 3.4
An
divides an angle into two congruent angles.
If a point is on the bisector of an angle, then it is
sides of the angle.
from the
Lesson 3.6
There is only one size of triangle that can be drawn with the segments
given, so the segments
the triangle.
Lesson 3.7
When three or more lines have a point in common, they are
.
Segments, rays, and even planes are
if they intersect in a
single point.
The three angle bisectors of a triangle are
point.)
(they meet at a
The three perpendicular bisectors of a triangle are
.
The three altitudes (or the lines containing the altitudes) of a triangle are
.
The point of concurrency for the three angle bisectors is the
.
The point of concurrency for the three perpendicular bisectors is the
.
The point of concurrency for the three altitudes is the
The
The
of a triangle is equidistant from the vertices.
of a triangle is equidistant from the sides.
.
A circle is
about a polygon if and only if it passes
through each vertex of the polygon.
A circle is
in a polygon if and only if it touches each side of
the polygon at exactly one point.
Lesson 3.8
The three
of a triangle are concurrent.
The point of concurrency of the three medians is the
.
The
of a triangle divides each median into two parts so that
the distance from the
to the vertex is
the distance
from the
to the midpoint of the opposite side.
The
region.
of a triangle is the center of
of the triangular