1. SEGMENT AND ANGLE RELATIONSHIPS
Geometry Chapter 2.3
SEGMENT AND ANGLE RELATIONSHIPS

2. Goal 1: Building Your Geometric Vocabulary
Definition of congruence
Congruent segments
Definition of a Segment bisector
Definition of Midpoint
Distance formula
Congruent angles
Angle bisector
Perpendicular to a line
Perpendicular to a plane

3. 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. 

4. 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.

5. Congruent segments
Two segments that are congruent have the same length. We mare congruent segments with “tic” marks.

6. Congruent Segments mean equal length
If two segments are congruent, then they have the same measure.
Because of the definition of congruence.

7. 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.
Because of the definition of congruence.

8. 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.
is a ray that cuts
into two congruent segments
and
Therefore,
is a segment bisector.

9. 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.
Ray BD bisects ABC. Ray BD is called an angle bisector.

10. Definition of Midpoint
The midpoint of a segment is the point that divides the segment into two congruent segments.
Midpoint formula
If C is the midpoint of segment AB,
then AB = CB.

11. Definition of perpendicular
Two lines are perpendicular
if they intersect to form a right angle.
A line is perpendicular to a plane
if it is perpendicular to each line in the plane
that intersects it.

12. Distance Formula
The distance between two points A(xA,yA) and B(xB,yB) is