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Geometry 101

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Geometry 101 - Page Text Content

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FC: Geometry 101 | - | Math tastes funny.... .... | Deena Asghar Period 5

1: Table of Contents | 1 | What is Geometry?........................................................................................................................................... 2 Polygons....................................................................................................................................................................... 3 Measuring and Drawing Angles....................................................................................................... 4 Planes.............................................................................................................................................................................. 5 Constructions.......................................................................................................................................................... 6 Arcs and Angles................................................................................................................................................ 7 Inverse, Converse, and Contrapositive...................................................................................... 8 Points of Concurrency ................................................................................................................................ 9 Inductive Reasoning...................................................................................................................................... 10 Deductive Reasoning.................................................................................................................................... 11 Conditional Statements and Truth Tables............................................................................... 12 Investigating Triangles................................................................................................................................ 13 Isosceles and Equilateral Triangles................................................................................................ 14 Writing Linear Equations........................................................................................................................... 15 Slope............................................................................................................................................................................... 16 Statements and Truth Values................................................................................................................. 17 The Polygon Sum Conjecture............................................................................................................... 18 The Properties of an Isosceles Triangle.................................................................................... 19 Special Angles from Parallel Lines.................................................................................................. 20 Finding the nth Term..................................................................................................................................... 21 Disjunctions and Conjunctions............................................................................................................ 22

2: What is Geometry? | The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. | Example of Parallel Lines and geometric shapes | 2

3: You don't say.. | POLYGONS | A plane figure with at least three straight sides and angles, and typically five or more. | WARNING: A CIRCLE IS NOT A POLYGON | A REGULAR POLYGON HAS ALL SIDES AND ANGLES EQUAL | 3

4: Measuring and Drawing Angles | 4 | In order to measure and draw angles you need geometric tools. To measure angles you need a protractor. In order to draw an angle, you will need a compass.

5: Planes | A flat surface on which a straight line joining any two points on it would lie. | A plane has no thickness but extends indefinitely in all directions. | A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC). | 5

6: constructions | angle bisector | perpendicular bisector | In order to do constructions, you basically need a compass and a straightedge | 6

7: Arcs and Angles | ANGLE: The space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet. | ARC: A part of the circumference of a circle or other curve. | MINOR ARC: Minor Arc is smaller of the two arcs formed when a circle is divided into two unequal parts. | Major ARC: Minor Arc is the larger of the two arcs formed when a circle is divided into two unequal parts. | 7

8: INVERSE, CONVERSE AND CONTRAPOSITIVE | (1) statement: if p then q (2) converse: if q then p (3) inverse: if not p then not q (4) contrapositive: if not q then not p (5) Negation: P and not Q | Remember: The contrapositive is the mixing of the inverse and the converse. | inverse: negation of both statements converse: reversal of both statements contrapositive: reversal and negation of both statements negation: contradicts the implication | 8

9: Point of Concurrency | Incenter | Circumcenter | Orthocenter | The point of intersection of the concurrent lines,segments, or rays. | 9

10: Geometry | It is the process of observing data, recognizing patterns and making generalizations about those patterns | INDUCTIVE REASONING | Used to prove or establish that a given statement is true based on a pattern of specific examples or past events

11: is the process of showing that certain statements follow logically from agreed upon assumptions and facts | Deductive Reasoning | PHOTOGRAPHY | The photography club helps students form an appreciation for the art of photography. We love taking photos! | 11

12: Statements: Conditional: if p, then q Converse: if q, then p Inverse: if not p, then not q Contrapositive: if not q, then not p | Conditional Statements and Truth Tables | 12

13: Investigating Triangles | equilateral triangles | isosceles triangle | scalene triangles | right triangles | 13

14: Isosceles and Equilateral Triangles | Isosceles Triangle: A triangle with two congruent sides | Equilateral triangle: a triangle with all sides and angles congruent | isosceles ----> <---- Equilateral | 14

15: Writing Linear Equations | Rise | Run | formula for slope | y=mx+b | slope-intercept form | we know, we know | 15

16: SLOPE | RISE | RUN | FUN FACT:Rene Decartes provided a method to solve the problem of lines and slopes in mathematics by his knowledge in Algebra and Geometry. | M=(X1+X2,Y1+Y2) | 2 2 | A surface of which one end or side is at a higher level than another. | 16

17: statements & | truth values | truth tables: A diagram in rows and columns showing how the truth or falsity of a proposition varies with that of its components. | statements:A definite or clear expression of something in speech or writing | 17

18: The sum of the measures of the n interior angles of an n-gon is 180(n-2) | 180 (n-2) | The polygon sum conjecture | 18

19: The Properties of an Isosceles Triangle | A triangle is isosceles if it has two congruent sides | Triangle Art | If a triangle is isosceles, then its base angles are congruent | 19

20: SPECIAL ANGLES FROM PARALLEL LINES | the opposite angles of a parallelogram are congruent the consecutive angles of a parallelogram are supplementary | 20

21: Finding the Nth Term | In order to find a pattern between terms, you can use inductive reasoning. then you would find a difference between consecutive terms. | if you needed to lets say find the 200th term of the sequence, you would use a rule that gives the nth term which is a function rule. | 21 | find the nth term f

22: A conjunction is a compound sentence that is formed by connecting two simple sentences using the word and. | Disjunctions and Conjunctions | A disjunction is a compound sentence that is formed by connecting two simple sentences using the word or | original statements | a compound statement can be made by joining simple statements with connectives such as and, or, and if then | 22

23: - | - | Geometry 101 | by: Deena | Asghar | ____

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  • By: Deena A.
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  • Title: Geometry 101
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  • Started: almost 4 years ago
  • Updated: almost 4 years ago

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