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Section 1.2-1.3 Definition Dense-Numbers go on forever and there are an infinite number of numbers between two numbers. Section 1.8 Postulates Uniqueness property-There is an exact distance between two points. Additive property-If B is between line AC then AB+BC=AC. Definition Betweenness-The number between two other numbers if it is greater than one of them and less than the other Section 2.1 Definitions Convex figure-A figure with no holes or dents in the side of the figure IFF- If and only if Conditionals => Flip the hypothesis and conclusion example: p=>q Bi-conditionals ⇔ If and only if the conditional and converse are true Union-The values between two numbers Intersections-The values that are common between two numbers Section 3.1-3.3 Definitions Angle Bisector-A ray that goes between angles Complementary angles-Two angles that equal 180 degrees Supplementary angles-Two angles that equal 90 degrees Adjacent angles- Two rays that end with a common end point. Linear pair- Two adjacent angles that are on non-common sides and opposite rays Vertical angles- Non-straight angles when the union of their sides equal two lines. Theorems Linear pair theorem- Two angles that form a linear pair, they are supplementary Vertical angles theorem- Two angles that are vertical, then they are equal Postulate Angle addition postulate- <ABD+<DBC=<ABC Section 3.4 Postulates Reflexive property- a=a Symmetric property- If a=b, then b=a Transitive property- If a=b and b=c then a=c Substitution property- If a=b and b=c then a can equal c Multiplication property- Multiply or divide both sides an equation by the same number Section 3.5 Definitions Justifications- 3 types, Postulates, property and definition Section 3.6 Theorem C.A.P- Two lines are parallel if corresponding angles created by a transversal are equal. Definition Transversal- A line that intersects two other lines Section 3.7 Theorems Parallel and slope theorem- Slopes of parallel lines are equal Perpendicular and slope theorem- Slopes of perpendicular lines are opposite reciprocals Section 3.8 Theorems Two perpendicular theorem- Two coplanar lines are each perpendicular to the same line, they are parallel. Perpendicular to parallel theorem- If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. Section 4.1 Definition Transformation- Two sets of points that each point in preimage set Section 4.2 Postulate Reflection Postulate- Reflection preserve: Angle measure, betweenness co-linearity, distance Section 4.4 Definition Composite- The first transformations of a figure, then an additional transformation Magnitude- The distance between two points Section 4.6 Definition Vector – Magnitude and direction of a translation Section 4.7 Definition Isometric- Reflection or composite of a reflection Section 5.5 Theorem Figure reflection theorem- The reflection image is corresponding if the angle has reflected points Section 5.6 Definitions Auxiliary Figures- Objects we add to a diagram to prove a statement Uniqueness- One and exactly one point or definition Section 5.7 Theorem Triangle Sum Theorem- The sum of the angles measure of three angles is 180 degrees. Any other polygon- 180(n-2) N=number of sides