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Basic Geometry Definitions . Point – a point . Line – a collection of points that continue forever in 2 directions . Line Segment – a collection of points with a definite beginning and end . Ray – directed line segment . Angle – 2 rays that converge on one point . Vertex – where 2 rays meet . Plane – the area in 2 dimensional object
Geometry 15 Chapter 2 – Reasoning and Proof Terms, Postulate and Theorems 2.1 Inductive Reasoning: looking at several specific situations to arrive at a conjecture. Conjecture: an educated guess. Counterexample: a false example; an example that proves a conjecture false. Conditional Statement: A statement that can be written
Definitions. Geometric mean. Definition. The value of x in proportion a/x = x/b where a, b, and x are positive numbers (x is the geometric mean between a and b) Sine, sin. For an acute angle of a right triangle, the ratio of the side opposite the angle to the measure of the hypotenuse. (opp/hyp) Cosine, cos.
Basic Geometric Terms. Point – an exact location in space. A point has no dimension. Line – a collection of points along a straight path that extends endlessly in both directions. Line Segment – a part of a line having two endpoints. (read “line segment ”) The length of is denoted . Ray – a part of a line having only one endpoint.
Statements of definitions are always true, as are their converses. Euler diagram for → ( b (a) ) A syllogism is a type of direct proof of the form a b b c Therefore, a c. The statements a b and b c are called the premises of the argument. a c is called the conclusion of the argument, and is often considered to be a theorem.
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Postulate #1: Given any two distinct points, there is exactly one (straight) line containing those two points. Postulate #2: Given any three non-collinear points, there is exactly one plane containing those three points. Postulate #3: If a line and a plane share two points, then the entire line lies within the plane.
Using postulates and math properties, we construct a sequence of logical steps to prove a theorem. I. A Straight Angle is 180 180 Il. Supplementary Angles add up to 180 m A+mLB=180 Example: 110 xyr and L ryz are supplementary angles. And, although they are not adjacent, LS and xyr are supplementary as well. B
