Section 2.1Exploring Patterns

Reasoning in geometry consists of 3 stages:(1) Look for a pattern(2) Make a conjecture – a guess as to what you think is happening (3) Verify the conjecture – use logical

reasoning to verify that it is true in ALL cases.

First 2 steps are inductive reasoning. The third step is when you are proving it.

Important Definitions:

Undefined terms: Point, Line, and Plane

Line Segment: AB consists of the endpoints A and B and all points on line AB that lie between A and B.

Line segment AB or BA

Defns cont.Ray – consists of an initial point (A) and all of the points on the line that lie on the same side of A that B lies. If C is between A and B, then are opposite rays.

Ray AB

Opposite rays CA and CB

A C B

Points, segments, or rays that lie on the same line are collinear. In the line above, the following are collinear:A,B,C ; AC, CB, AB ; AC, CB, BC

An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The angle that consists of the rays AB and AC is denoted by <BAC, <CAB, or <A. The point A is the vertex of the angle.

The measure of <A is denoted by m<A. Angles are classified as acute, right, obtuse, and straight.

Right : m<A = 90o

Acute : 0o < m<A < 90o

Obtuse : 90o < m<A < 180o

Straight : m<A = 180o

Interior – a point is on the interior of an angle if it lies in between the points that lie on each side of the angle.

exterior – lies on the outside of the sides of the angle.

Two angles are adjacent if they share a common vertex and side, but have no common interior points.

Angle ABC is adjacent to angle CBD

Because:

they have a common side (line CB)they have a common vertex (point B)