Presentation on theme: "Proving Statements in Geometry"— Presentation transcript:
1Proving Statements in Geometry Inductive Reasoning
2The 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.
3Basic Definitions inEuclidean GeometryThe 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.
4A LineAn infinite set of points.A PlaneA set of 3 or more non collinear points.
5Collinear set of points A set of points that lie on the same straight line.Non-collinear pointsPoints 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.
6B is said to be between A and C if and only if AB+BC=AC BetweenessB is said to be between A and C if and only if AB+BC=ACBCALine SegmentAll points on a line between 2 endpoints.ABCongruenceEqual in measure and similar in shape.
7Segments that have the same measure Congruent segmentsSegments that have the same measure( we assume all lines have the same shape).ABCSegment AB is the same length as segment BC so they are congruent segments.
8Midpoint of a line segment A point that divides a line segment into 2 congruent line segments,Bisector of a line segmentA line that divides a line segment into 2 congruent line segments.
92 rays that lie on the same line and share a common endpoint. A Rayis 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 Rays2 rays that lie on the same line and share a common endpoint.
102 rays that share a common endpoint called the vertex An Angle2 rays that share a common endpoint called the vertexBVertexAC
11Types of Angles Straight Angle An angle that is the union of 2 opposite rays, it’s measure equals 180 degrees.An acute angleis an angle “A” whose degree measure isbetween 0<A<90.
12A right AngleIs an angle that measures 90 degrees.An Obtuse AngleIs an angle whose measure is between90<A<180 degrees.
13An Oblique AngleIs an angle whose measure is between180<A<360 degrees.an angle that is not a right angle or any multiple of a right angle
14Congruent anglesHave the same degree measure and the same shape.A Bisector of an AngleIs a ray whose endpoint is the vertex of the angle and divides the angle into 2 congruent parts.
15A 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.