Building Blocks of Geometry

The Building Blocks Point Plane Line These 3 objects are used to make all of the other objects that we will use in Geometry What do you think it means to be a “Building block of Geometry? What might one be?

Point The most basic building block Has no size Only has a Location Representation – Shown by a Dot – Named with a single Capital letter Ex: What would a real world example be? = “Point P”

Line A straight, arrangement of infinitely many points. Infinite length, but no thickness Extends forever in 2 directions Named by any 2 points on the line with the line symbol above the letters (order does not matter Ex: = “Line AB” or “Line BA” Real World Example?

Plane An imaginary flat surface that is infinitely large and with zero thickness Has length and width, but no thickness It is like a flat surface that extends infinitely along its length and width Represented by a 4 sided figure, like a tilted piece of paper – This is really only part of a plane Named with a Capital Cursive letter Ex: = “Plane P” Real World Example?

Explaining the Objects Can be difficult Early Mathematicians attempted to: Ancient Greeks “A point is that which has no part. A line is a breathless length.” Ancient Chinese Philosophers “The line is divided into parts, and that part which has no remaining part is a point.”

What’s the Problem?

Definitions A definition is a statement that clarifies or explains the meaning of a word or phrase It is impossible to define “point,” “line,” and “plane” without using words or phrases that need to be defined. Therefore we refer to these building blocks as “Undefined” Despite being undefined, these objects are the basis for all geometry Using the terms “point,” “line,” and “plane,” we can define all other geometry terms and geometric figures

Definitions Collinear – Lie on the same line – Example – Points A and B are “Collinear”

Definitions Coplanar – Lie on the same plane – Example – Point A, Point B, and Line CD are “Coplanar.”

Definitions Line Segment – Two points (called endpoints) and all of the points between them that are collinear. – In other words, a portion of a line – Represent a Line Segment by writing its endpoints with a bar over the top – Example:

Definitions Ray – Begins at a single point and extends infinitely in one direction – Example: – You need 2 points to name a ray, the first is the endpoint, and the second is any other point that the ray passes through.

Definitions Congruent – equal in size and shape – We mark 2 congruent segments by placing the same number of slash marks on them. – The symbol for congruence is and you say it as “is congruent to.” – Example:

Definitions Bisect – Divide into 2 congruent parts Midpoint – the point on the segment that is the same distance from both endpoints. The midpoint bisects the segment

Definitions Parallel Lines – 2 lines that never intersect – We mark 2 lines as parallel by placing the same number of arrow marks on them. – Example: – To write this as a statement, we would write

Definitions Perpendicular Lines – 2 lines that intersect at a Right Angle (90°). – We mark 2 lines as Perpendicular by placing a small square in the corner where they cross – Example: – To write this as a statement, we would write:

Things you may Assume 1)You may assume that lines are straight, and if 2 lines intersect, they intersect at 1 point. 2) You may assume that points on a line are collinear and that all points & objects shown in a diagram are coplanar unless planes are drawn to show that they are not coplanar.

Things you may NOT Assume 1)You may not assume that just because 2 lines, segments, or rays look parallel that they are parallel – they must be marked parallel 2)You may not assume that 2 lines are perpendicular just because they look perpendicular – they must be marked perpendicular 3)Pairs of angles, segments, or polygons are not necessarily congruent, unless they are marked with information that tells you that they are congruent.