Proving Statements in Geometry Inductive Reasoning

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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

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

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.

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.

A triangle Is a polygon with exactly 3 sides.

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