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FC: My | Geometry | IN REVIEW | YEAR | 2013 | By: Oksana Pligina
1: T A B L E OF C O N T E N T E S | IS WHEREVER WE ARE, BUT WE CURRENTLY LIVE IN | PAGES 2. Midpoints 17. Special Angles 3. Measuring & Drawing Angles from Parallel Lines 4. Defining Angles 18. Slopes of Parallel 5.Polygons & Perpendicular Lines 6. Investigating Triangles 19. Properties of 7.Identifying Quadrilaterals Isosceles Triangles 8. Circles & Arcs 20. Points of 9. Planes Concurrency 10. Inductive Reasoning 11. Finding the nth Term 12. Statements & Truth Values 13. Disjunctions & Conjunctions 14. Biconditional 15. Inverse, Converse, & Contrapositives 16. Angle Relationships
2: Midpoints | A Midpoint is a point on a line segment that divides it into two equal parts
3: Measuring & Drawing Angles | To measure and draw an angle, you would have to use a protractor. | Steps to measure: 1. Place the center mark of the tool on the vertex 2. Line up the 0-mark with one side of the angle 3. Read the protractor on the protractor scale 4. Make sure that you are using the right scale! | To draw an angle you would have to draw a straight line, make a vertex, and make a line heading towards the degree you want your angle to be.
4: Defining Angles | There are seven types of angles that we have discussed this year: right, acute, obtuse, complementary, vertical, linear pair, and supplementary. | Right angles measure exactly 90 degrees. Acute angles measure anywhere from above 0 to below 90 degrees. Obtuse angles measure anywhere from above 90 to below 180 degrees Complementary angles are two angles that add up to 90 degrees Vertical angles are formed when two lines intersect. These angles aren't adjacent & are equal in measure Supplementary angles are two angles which add up to 180 degrees A linear pair of angles are two adjacent angles that form a straight, 180 degree line
5: Polygons | A polygon is a closed figure that is formed by connecting line segments, with each segment joining exactly two others. | Such figures include: triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, decagons, undecagons, and dodecagons. | Polygons can be equilateral (all sides are equal), equiangular (all angles are equal), or regular which means that they are both equiangular and equilateral.
6: Investigating Triangles | Another triangle is the acute triangle where all of the angles in the triangle are less than 90 degrees
7: Identifying Quadrilaterals | A kite is a quadrilateral with two pairs of consecutive congruent sides. | A parallelogram is a quadrilateral with two pairs of parallel sides, opposite sides are congruent and opposite angles as well.
8: Circles & Arcs | A circle is a set of points that are equidistant from a point called the center. The circle includes a radius, diameter, chord, and tangents. | Arcs are the distance between any two points on the circumference on a circle. | There are many types of arcs as well, including a semicircle, major, and minor arcs.
9: Planes | A plane has a length and width, but no thickness. It is like a flat surface that extends infinitely along its length and width. | Things to Know: The intersection of two different planes is a line. If two parallel planes are both intersected by a third plane, then the intersections of the three planes are parallel lines.
10: Inductive Reasoning | Inductive reasoning is a type of reasoning that allows you to make conclusions based on a pattern of specific examples or past events. | A conclusion reached by inductive reasoning is a conjecture
11: Finding the nth Term | A sequence is a set of terms in a definite order, where the terms are obtained by a rule. The nth term is an unknown number in a sequence. A rule that gives the nth term for a sequence is called a function rule.
12: Statements & Truth Values | A mathematical sentence expresses a complete idea or fact which can be true, false or have undetermined truth value. A closed sentence can be judged true or false. An open sentence has a truth value that cannot be determined. | A negation of a statement can usually be formed by placing the word "not" into the original statement. The symbol used is "~". | Examples: Garfield is a cartoon character (T.) The NY Giants did win the game (F.) | Note: Two negations return the truth value of a sentence to its original value.
13: Disjunctions & Conjunctions | A conjunction is a compound statement formed by joining two or more simple statements with the word "and." Example: Let p represent "It is Tuesday." and let q represent "There is school tomorrow." The conjunction (p^q) is "It is Tuesday and there is school tomorrow." A disjunction is a compound statement formed by joining two or more simple statements with the word "or." Example: Let p represent "It is Tuesday." and let q represent "It is snowing." The disjunction (pVq) is "It is Tuesday or it is snowing."
14: Biconditional | A biconditional statement is a statement that contains the phrase "if and only if" (iff). Writing one is the same as writing a conditional statement and it's converse. Example: Given: 1. A polygon is a quadrilateral 2. It has four sides Biconditional: A polygon is a quadrilateral if and only if it has four sides. | Note: The notation is p <-> q
15: Inverse, converse, and Contrapositives | An inverse statement is formed by negating both the hypothesis and conclusion. Example: If you are not 15 years old, then you are not a teenager. | A converse statement is formed by switching the hypothesis and conclusion. Example: If you are a teenager, then you are 15 years old. | A contrapositive is a statement formed by switching and negating the hypothesis and the conclusion. Example: If you are not a teenager, then you are not 15 years old. | Note: The hypothesis is the "if" and the conclusion is the "then." These make up the conditional statement.
16: Angle Relationships
17: Special Angles on Parallel Lines | When cut by a transversal, parallel lines form five types of special angles: corresponding, alternate interior, alternate exterior, vertical, and a linear pair of angles | Corresponding angles are the "matching corners" on parallel lines. They can also be congruent. | Alternate interior angles are inside the parallel lines on opposite sides cut by the transversal. Alternate exterior angles are outside the parallel lines on opposite sides of the transversal.
18: Slopes of Parallel & Perpendicular Lines | The slopes of parallel lines have the same slope and different y-intercepts. | The slopes of perpendicular are the negative reciprocal of each other. Example: 1/2x and -2x
19: Properties of Isosceles Triangles | Isosceles Triangle Conjecture: If a triangle is isosceles, then its base angles are congruent. | An isosceles triangle is a triangle that has two equal sides. | It is made up of four different parts: the legs, base, base angles, & the vertex angle. | The base angle is the bottom of the triangle that includes the base angles that are also congruent. | The vertex angle is the non-congruent angle on the tip of the triangle. The legs are the two congruent sides of the triangle
20: Me going to school this week. | Every project needs a Danny DeVito. | (or eight.)