Geometry Chapter 2 REASONING. Geometry Chapter 2 : REASONING Exploring Patterns The structure of geometry Segment and Angle relationships Conditional.

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Presentation transcript:

Geometry Chapter 2 REASONING

Geometry Chapter 2 : REASONING Exploring Patterns The structure of geometry Segment and Angle relationships Conditional Statements Reasoning with properties from algebra Deductive reasoning

2.1 Exploring Patterns Goal #1 – Identifying Patterns Inductive Reasoning Strategies (Induction occurs when we gather bits of specific information together and use our own knowledge and experience in order to make an observation about what must be true.) Observation: John came to class late this morning. Observation: John’s hair was uncombed. Prior experience: John is very fussy about his hair. Conclusion: John overslept

IDENDIFYING PATTERNS Given the following table write a conjecture (educated guess) about the pattern n12345n S

How about a picture? n12345n S

Goal #2 – reading and using definitions PointLineLine segment RayOpposite ray Collinear AngleAcuteRight ObtuseStraightInterior ExteriorAdjacentPlane 2.1 Exploring Patterns

Definitions Postulates Theorems Axioms Properties Constructions Rules for providing proof

Point (A) : not a defined term in geometry (we just think about it being a dot in space or in a plane) A point is represented by a capital letter A

not a defined term in geometry (think about it being an infinite number of points connecting in a straight orientation moving in both directions forever) A line is represented by two points and a line with two arrow heads on each end AB Line:

part of a line with two endpoints A line is represented by two points and a line with two points on each end AB Line Segment:

part of a line that has one endpoint A ray is represented by one points and a line with one arrow head AB Ray

Opposite Rays An opposite ray is represented by a shared endpoint points and a line with one arrow head pointing in the opposite direction A BC

Collinear: When points lie on the same line they are collinear. The word betweenness in geometry implies that all points are collinear AB C A lies between C and B. A, B, C are collinear.

Angles An angle is created by two rays that have a common endpoint AB C Each ray is called the side of the angle. The common Endpoint is called the vertex of the angle. The amount of rotation about the vertex is called the measure of the angle. Common units of measurement of angles are degrees and radians.

Parts of an angle Angles are written with either the vertex point [if no other angles share this vertex] or a point on one of the rays, the vertex, and the point on the other ray. AB C Interior of angle Exterior of angle

Types of angles Acute Obtuse Right Straight 0 o < acute < 90 o 90 o < obtuse < 180 o right = 90 o Straight = 180 o

Adjacent angles AB C  DAC is NOT adjacent to  BAD  DAC is adjacent to  BAC D

Angle measures