FC: Geometry Scrapbook By:Matthew Morgani Period 5 Mrs.Salke
1: Table of Contents Page 1-Logic Page 2-Geometry basics Page 3-Triangle Congruence Proofs Page 4- Parallel Lines & triangles Page 5- Quadrilaterals Page6- Coordinate Geometry Page 7- Graphing Systems & Circles
2: Logic | Logic: A set of rules by which conclusions are drawn. | Statement: Any sentence conveying information that can be judged true or false, but not both. | Conditional Statements: If-then statements | Overview
3: Logic | Converse: a statement that is formed by interchanging the hypothesis and conclusion of a conditional statement. | Biconditional Statement: a statement written in “if and only if” form. | Negation: a statement that is formed by denying another statement. | Inverse: a statement formed by negating both the hypothesis and conclusion of a conditional statement. | Contrapositive: a statement formed by interchanging the hypothesis and conclusion AND negating both | In the fifth century b.c., the Greeks used logic to expound on the political and ethical issues of the day.
4: Logic tables and Statements | A statement is an assertion that can be determined to be true or false. (contrapositive, inverse, converse)
5: Geometry Basics | A line has no beginning point or end point. Imagine it continuing indefinitely to both directions. We can illustrate that by little arrows on both ends. | A ray has a beginning point but no end point. Think of sun's rays: they start at sun and go on forever. | An angle is made up from two rays that have the same beginning point. That point is called the vertex and the two rays are called the sides of the angle.
6: Parallel lines are lines that never intersect or cross one another. | A line segment is a part of a line having two endpoints. | Perpendicular lines cross each other or intersect at right angles. | alternate interior angles are angles that are on the inside of the parallel lines and on opposite sides from each other. | alternate exterior angles are the angles on the outside of the parallel lines and on opposite sides of the transversal. | A transversal is a line or ray that divides other lines or rays
7: Every building, house or object is made up of angles. Even though they are different sizes and shapes, there are still many angles used to complete it. For an example, a room in any building is made up of right angles. Angles are something that might be over looked to the users, but to the engineer, angles are everything. | Real world connections
8: Triangle Congruence Proofs | Triangles that have exactly the same size and shape are called congruent triangles. | Side-Angle-Side is a rule used in geometry to prove triangles congruent. The rule states that if two sides and the included angle are congruent to two sides and the included angle of a second triangle, the two triangles are congruent. An included angle is an angle created by two sides of a triangle | Side-Side-Side - The rule states that if three sides of one triangle are congruent to three sides of a second triangle, the two triangles are congruent. | Angle-Angle-Side - The rule states that if two angles and a non included side of one triangle are congruent to two angles and the corresponding non included side of another triangle, the two triangles are congruent.
9: Angle-Side-Angle - The rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. An included side is a side that is common to (between) two angles. | When two triangles are congruent, all six pairs of corresponding parts (angles and sides) are congruent. This statement is usually simplified as corresponding parts of congruent triangles are congruent, or CPCTC for short. | Triangle proofs could be used my construction workers or maybe carpenters. knows that to triangles are the same or not can have a large effect on something or someone is building.
10: Parallel lines are lines in the same plane that never meet no matter how far they run. Parallel lines are always the same distance apart and always in the same plane. | Parallel Lines & Triangles | A plane is a flat surface that has length and width, but no thickness. | A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted \triangle ABC. | The angles in a triangle always add up to 180 degrees.
11: If two parallel lines are transected by a third, the alternate interior angles are the same size. | If a line intersects two other lines then... | * a) The alternate interior angles are the same size * b) The corresponding angles are the same size * c) The opposite interior angles are supplementary. | Two triangles are similar if and only if the ratios of their corresponding sides are all the same. | Structural frames of buildings, railroad tracks, windows (opposite sides), sailboats, steps, and paper. parallel bars in gymnastics Also anything that is shaped as a rhombus, square or a rectangle are all example of parallel lines in our world.
12: Quadrilaterals | A Quadrilateral is a polygon that has four sides. | A parallelogram is a quadrilateral having two pairs of parallel sides. | A rhombus is a quadrilateral of which all fours sides are the same length. | A rectangle is a parallelogram of which all four angles are 90 degrees.
13: A square is a quadrilateral of which all four sides are of the same length, and all four angles are 90 degrees. Its also a rectangle, a rhombus, and a parallelogram. | A trapezoid is a quadrilateral which has two parallel sides | Man-made structures that includes geometric structures would be almost everything. If a person looks closely, they would see many geometry in the structure. There are too many items to list. Buildings, cars, rockets, ships, windows, books, disks, plates are all geometric structures.
14: Coordinate Geometry | Coordinate geometry is geometry dealing primarily with the line graphs and the (x, y) coordinate plane. | Most of the questions on coordinate geometry focus on slope.The slope of a line is a measurement of how steeply the line climbs or falls as it moves from left to right. | If a line slopes uphill as you trace it from left to right, the slope is positive. If a line slopes downhill as you trace it from left to right, the slope is negative.
15: A midpoint is a point that denotes the middle of any given line segment. | Parallel lines are lines that don't intersect. In other words, parallel lines are lines that share the exact same slope. | Perpendicular lines are lines that intersect at a right angle. In coordinate geometry, perpendicular lines have negative reciprocal slopes. That is, a line with slope m is perpendicular to a line with a slope of –1/m. | distance-The length of the line joining the points (x1, y1) and (x2, y2) is:
16: Coordinate geometry can be used in a blue print for a home, or on a floor plan by a construction worker.
17: Graphing Systems and circles | When you are solving systems you are, graphically, finding intersections of lines. | To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution. | The graphing calculator can solve systems of equations graphically-
18: A circle is all the points that are the same distance, r called the radius, from a point, - called the center. | The center of the circle is the midpoint of the line segment. | The midpoint formula is used to find the coordinates of the center of the circle. | The radius is half the diameter. the diameter is the measure from one side of the circle, to the other.
19: A table of values is a list of numbers that are used to substitute one variable, such as within an equation of a line and other functions, to find the value of the other variable, or missing number.
20: The proof that girls are evil: First, we state that girls require time and money Girls = Time x Money And as we all know, "time is money" Time = Money Therefore, Girls = Money x Money = (Money)^2 And because "money is the root of all evil" Money = sqrt(Evil) Therefore: Girls = (sqrt(Evil))^2 And we are forced to conclude that: Girls = Evil | Math jokes :)
21: What do you say when you see an empty parrot cage? A Polygon | Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter? A: Pumpkin Pi! | A man walks up from the town and drags his son with him. He goes to a school and asks what they teach. Teacher- We teach everything sir. Reading , writing, arithmetic... Man- What is this ariththingy. Teacher- Well its maths, sir. We teach many things including stem and leaf diagrams and trigonometry. Man- Dang me, that's just what he needs, triggernometry. He's the worst shot in the family.