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Geometry Scrapbook

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FC: geometry scrapbook | Geometry is all around us; everyday and everywhere

1: TABLE OF CONTENT Constructions............................................................................. Page 1 Point of Concurrency........................................................... Page 2 Triangle Congruence............................................................. Page 3 Corresponding Parts of Congruent Triangles..... Page 4 The Triangle sum conjecture......................................... Page 5 Finding the nth Term.......................................................... Page 6 DIsjunction and Conjunction........................................... Page 7 Inverse, Converse, Contrapositives............................... Page 8 Deductive reasoning.............................................................. Page 9 Inductive reasoning.................................................................. Page 10 Angle Relationships.............................................................. Page 11 Special Angles from Parallel lines............................. Page 12 Defining angles......................................................................... Page 13 Polygons........................................................................................... Page 14 The Polygon sum Conjecture............................................ Page 15 Slope.................................................................................................... Page 16 Writing Linear Equations.................................................. Page 17 Solving System of Linear Equation............................. Page 18 Flowchart Proofs...................................................................... Page 19 Statement and truth values.............................................. Page 20

2: A construction is complete when it is designed with just a straightedge and a compass. Construction- a precise way of drawing with only two tools; a straightedge and a compass | In the picture to the left, there is a construction that was designed with just two tools. A compass and a straightedge. The compass was used to draw the circle and the straightedge was used to draw the Astrid. | CONSTRUCTION

3: When 3 lines intersects to form a point, it is called the point of concurrency. Point Of Concurrency- The point of intersection of the concurrent lines,segments, or rays | In the Points of Concurrency, there are four types of concurrency; Incenter, Circumcenter, Centroid, and Orthocenter.Incenter is formed when 3 angle bisectors intersect. Circumcenter is formed when 3 perpendicular bisectors intersects. Centroid is formed when 3 medians intersects. Last but not least, an orthocenter is formed when 3 altitude intersects. | POINT OF CONCURRENCY

4: A triangle is congruent when it follows the four rules. Ex: ASA,SAS,SSS, and SAA Triangle Congruence- In geometry, two figures are congruent if they have the same shape and size | In the following picture we know that angle A and angle D is congruent, line AC and line CD is congruent, and angle BCA and angle DCE is congruent because they are vertical angles. These triangles follows the rule ASA, therefore they are congruent triangles. | TRIANGLE CONGRUENCE

5: If a pair of triangle is congruent, they automatically follow the CPCTC rule. CPCTC- corresponding parts of congruent triangles are congruent'. It means that once we know that two triangles are congruent, we know that all corresponding sides and angles are congruent | CORRESPONDING PARTS OF A TRIANGLE

6: The sum of the angles in every triangle must add up to 180 degrees. Triangle sum conjecture- Sum of the measures of the three angles in a triangle | THE TRIANGLE SUM CONJECTURE

7: The nth term is the value that increases the original number The nth term- being the last in a series of infinitely decreasing or increasing values | FINDING THE NTH TERM

8: If a compound statement is formed with the word and then it is a conjunction. Conjunction-A conjunction is a compound statement formed by joining two statements with the connector "and | If a compound statement is formed with the word or then it is a disjunction. Disjunction- A disjunction is a compound statement formed by joining two statements with the connector "or". | CONJUNCTION AND DISJUNCTION

9: Truth values for Conditional Statements is formed by Converse, Inverse, and Contrapositive. Converse- q-->p Inverse- ~p-->~q Contrapositive- ~q-->~p | CONVERSE, INVERSE, CONTRAPOSITIVE

10: A deductive reasoning is formed when it is proved by facts and statements. Deductive Reasoning- reasoning from the general to the particular (or from cause to effect). | DEDUCTIVE REASONING

11: A inductive reasoning is formed when it is proved by a certain pattern. Inductive reasoning- reasoning from detailed facts to general principles. | INDUCTIVE REASONING

12: Angle relationships are formed by rays intersecting or touch each other. Angle Relationships- A shape, formed by two lines or rays diverging from a common point (the vertex). | ANGLE RELATIONSHIPS

13: In a pair of parallel line, special angles are formed. Supplementary angles, Complementary angles, vertical angles, alternate interior, alternate exterior, etc. Special Angles in parallel line- When parallel lines get crossed by another line (which is called a Transversal), many angles are the same | SPECIAL ANGLES FORMED BY PARALLEL LINES

14: Defined angles are formed when two rays meets at a certain point Defining Angles- the space within two lines or three or more planes diverging from a common point, or within two planes diverging from a common line. | REFLEX ANGLE (more than 180 degree less than 360 degree) | OBTUSE ANGLE(more 90 degree, less than 180 degree) | ACUTE ANGLE(more 0 degree, less than 90degree) | RIGHT ANGLE(90 degree) | DEFINING ANGLES

15: A polygon is formed when 3 or more line segments joins exactly next to each other. Polygon- A plane figure with at least three straight sides and angles, and typically five or more | POLYGONS

16: The polygon sum conjecture is found by (n-2)*180. Polygon Sum Conjecture- The sum of angle measures in polygons | THE POLYGON SUM CONJECTURE

17: The slope is found by m=Rise/Run in graphing or m=Y2-Y1/X2-X1. Slope- A surface of which one end or side is at a higher level than another. | SLOPE

18: A linear equation can only be written with the formula, y=mx+b. Linear equation- a first order equation involving two variables: its graph is a straight line in the Cartesian coordinate system. | WRITING LINEAR EQUATION

19: A system of equation is solved by these two following; Elimination and Substitution Elimination-the process of eliminating one of the variables in a system of equations using addition or subtraction in conjunction with multiplication or division and solving the system of equations. Substitution- A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable. | SOLVING SYSTEM OF LINEAR EQUATION

20: Flowchart proofs are organized with boxes and arrows; each "statement" is inside the box and each "reason" is underneath each box. Flowchart proof- a graphical way of showing the logical steps used to demonstrate some mathematical claim. | FLOWCHART PROOF

21: Statement and truth values are found when a statement is true or false. Statement Truth Values- either of the values, true or false, that may be taken by a statement | STATEMENTS AND TRUTH VALUES

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• By: Fiona T.
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