Part 1: Concepts King For Maths / Best Trick to Learn Concepts:
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Lecture 1: Introduction - Points, Segments, and Length
Geometry is a science of space. The name "Euclid" (the Father of Modern Geometry) is synonymous with all geometric disciplines, such that his thirteen books on Elements are considered to be one of the most important and influential works in the history of mathematics.
Lecture 1:
Point - An infinitesimally small single. Location in space which has no length, width, or height, only a location.
Line Segment - Consists of two points called endpoints, and all the points between the endpoints.
A line segment is a finite distance between two points.
Lecture 2: Pythagorean Theorem and Distance Formula
Example 1: Find the distance between the following points.(P and Q)
This is segment PQ, denoted PQ.
Line - A set of points that extends infinitely in both directions. It has infinite length, and zero width and height. A straight line is the shortest distance between two points.
When writing the name of an angle, the point at the vertex always appears in the middle of the name.
Plane: A very big flat region. A plane goes on forever in four directions up, down, left, and right. It looks kind of like a tabletop, except that it goes on and on forever.
Plane
In geometry, we will draw a plane like this. We must remember. However, that a plane continues forever in all four directions; this drawing shows only a portion of the actual plane.
EXAMPLE:
Statement: If this animal is a collie, it is a dog.
Converse: If this animal is a dog. Then it is a collie.
Statement: If P, then Q.
Converse: If Q, then P.
It is possible for an implication to be true while its converse may not be true. Remember, if the statement is expressed in the form "If P, then Q", the converse is "If Q, then P".
: Postulates and Proofs
"Every Friday we will have a quiz."
-- by deductive reasoning
We can rewrite the above statement in the form of an implication: "If it is Friday, then we will have a quiz."
Now, suppose you are given two points, P and Q. How many lines can be drawn to connect P and Q? Only one line. This is known as a postulate.
A postulate is a very basic statement that we assume to be true.
Using postulates, by deductive reasoning, we prove theorems. A theorem is proved to be true using deductive reasoning.
Point: A point is a specific location in space. The point is named with an upper case letter and represented by a dot, such as "point A."
Line: A line is a series of points that continue into infinity without endpoints. Arrows at the end of a line indicate that the line extends forever. Adding two random points to the line and naming the points "A" and "F" results in line "AF."
Line Segment: In high school geometry, you will deal with many line segments. As opposed to a line that continues forever, a line segment has two endpoints. The endpoints could be named "A" and "F."
Ray: Think of a ray of light coming from the sun. It has an endpoint (the sun) and continues forever into space away from the sun or endpoint.
Angle: An angle is simply two rays with the same endpoint, creating an angle or "v" shape.
Vertex: The vertex is the point where two rays meet.
