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**Proving Statements in Geometry**

Inductive Reasoning

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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.

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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.

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

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**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.

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**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.

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**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.

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**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.

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**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.

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**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

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**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.

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

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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

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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.

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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.

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A triangle Is a polygon with exactly 3 sides.

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Homework Worksheet

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California State Standards 1. Understand and Use undefined terms, axioms, theorems, and inductive and deductive reasoning 15. Use the Pythagorean Theorem.

California State Standards 1. Understand and Use undefined terms, axioms, theorems, and inductive and deductive reasoning 15. Use the Pythagorean Theorem.

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