Download Geometry Chapter 2.3

Geometry Chapter 2.3
SEGMENT AND ANGLE
RELATIONSHIPS
Goal 1: Building Your
Geometric Vocabulary
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Definition of
congruence
Congruent segments
Definition of a
Segment bisector
Definition of
Midpoint
Distance formula
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Congruent angles
Angle bisector
Perpendicular to a
line
Perpendicular to a
plane
Definition of congruence
If two objects have the exact same
shape (are line segments, rays, lines,
angles, triangles, polygons, etc.) and
they have the exact same measurement
(distance, angle measure, etc.) then
they are congruent.
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Definition of congruence
Definitions can be interpreted both
ways (forward or backward), in
other words if two segments have
the same measure, then they are
congruent AND if two segments are
congruent, then they have the
same measure.
Congruent segments
Two segments that are congruent have the
same length. We mare congruent segments
with “tic” marks.
B
D
A
C
AB  CD
Congruent Segments mean
equal length
If two segments are congruent, then
they have the same measure.
If AB  CD,
B
D
A
then AB  CD
C
Because of the definition
of congruence.
Congruent angles
Congruent angles have the same measure.
We mark their equal angles by using the
same number of arcs. (Please place an arc
on each of the angles drawn below.)
If two angles are congruent, then they
have the same measure.
IfABC  EFG,
A
F
thenmABC  mDEF
B
C
E
D
Because of the definition
of congruence.
Segment bisector
A segment bisector is any point, line, line segment, ray,
or plane that intersects a line segment to create two
smaller line segments that have equal length.
A
is a ray that cuts
BD
D
AC
into two congruent segments
B
C
AB
and
BD
BC
Therefore,
is a segment bisector.
Angle Bisector
An angle bisector is any line, line segment, ray, or plane
that intersects an angle at its vertex to create two
smaller angles that have equal measurements.
A
D
B
C
Ray BD bisects ABC.
Ray BD is called an angle
bisector.
Definition of Midpoint
The midpoint of a segment is the point that divides the
segment into two congruent segments.
A
Midpoint formula
C
B
 x  xB y A  y B 
C A
,

2
2

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If C is the midpoint of segment AB,
then AB = CB.
Definition of perpendicular
Two lines are perpendicular
if they intersect to form a right angle.
A
B
A line is perpendicular to a plane
if it is perpendicular to each line in the plane
that intersects it.
C
Distance Formula
The distance between two points A(xA,yA) and B(xB,yB) is
xA  xB    y A  yB 
2
2