1. Proving Statements in Geometry
Inductive Reasoning

2. The method of reasoning in which a series of examples leads to a general truth is called inductive reasoning.
An example would be a scientific experiment, where a number of experimental trials leads to a general conclusion.

3. Basic Definitions in
Euclidean Geometry
The undefined term in geometry is a point.
We can draw it.
We can see it but we can not define it.
But from this undefined term we can define other important words in geometry.

4. A Line
An infinite set of points.
A Plane
A set of 3 or more non collinear points.

5. Collinear set of points
A set of points that lie on the same straight line.
Non-collinear points
Points that do not lie on the same straight line.
The distance between 2 points on the number line is the absolute value of the difference between the 2 coordinate points.

6. B is said to be between A and C if and only if AB+BC=AC
Betweeness
B is said to be between A and C if and only if AB+BC=AC B C A
Line Segment
All points on a line between 2 endpoints. A B
Congruence
Equal in measure and similar in shape.

7. Segments that have the same measure
Congruent segments
Segments that have the same measure
( we assume all lines have the same shape). A B C
Segment AB is the same length as segment BC so they are congruent segments.

8. Midpoint of a line segment
A point that divides a line segment into 2 congruent line segments,
Bisector of a line segment
A line that divides a line segment into 2 congruent line segments.

9. 2 rays that lie on the same line and share a common endpoint.
A Ray
is a part of a line that has only one endpoint.
In Geometry, a ray starts at one point, then goes on forever in one direction.
Opposite Rays
2 rays that lie on the same line and share a common endpoint.

10. 2 rays that share a common endpoint called the vertex
An Angle
2 rays that share a common endpoint called the vertex B
Vertex A C

11. Types of Angles Straight Angle
An angle that is the union of 2 opposite rays, it’s measure equals 180 degrees.
An acute angle
is an angle “A” whose degree measure is
between 0<A<90.

12. A right Angle
Is an angle that measures 90 degrees.
An Obtuse Angle
Is an angle whose measure is between
90<A<180 degrees.

13. An Oblique Angle
Is an angle whose measure is between
180<A<360 degrees.
an angle that is not a right angle or any multiple of a right angle

14. Congruent angles
Have the same degree measure and the same shape.
A Bisector of an Angle
Is a ray whose endpoint is the vertex of the angle and divides the angle into 2 congruent parts.

15. A polygon is a closed figure in a plane that is the union of line segments that intersect only at their endpoints and no 2 segments are collinear.

17. A triangle
Is a polygon with exactly 3 sides.

18. Homework
Worksheet