Building Blocks of Geometry Because without geometry… life is pointless

Geometry started as… Began as the study of the earth measure There had to be some way to use language to describe the world in terms of numbers because of the need to measure the Earth.

Geometry means… the word geometry derives from the Greek geo (earth) from the very ancient Greek Earth Goddess Gaia and from the word metron which means to measure (the word meter is also derived from it)

Today Geometry is … the study of one dimensional objects such as lines and segments. the study of the properties of two dimensional shapes such as triangles, quadrilaterals and circles. The study of the three dimensional shapes such as cylinders, pyramids and cones.

Euclid (Greek,400 BC) Euclid established the basic rules for constructions using only a compass and straight edge. Euclid proposed definitions and constructions about points, lines, angles, surfaces and solids.

Deductive System Euclidian constructions are used to study properties of lines and shapes. Euclid created a deductive system to organize geometry properties utilizing: Premises (accepted facts)…postulates Logical Rules (rules that can be proven)…theorems

Building Blocks of Geometry There are three building blocks of geometry which are referred to as the undefined terms. They are the foundation of all the geometry: Point Line Plane

In Geometry all definitions are based on the terms… point, line and plane Using these undefined terms, you are able to define all other geometry terms and figures.

First Undefined Term: Point The most basic building block of geometry. It has no size. It has only location. You represent a point with a dot A ● Note: you name a point with a single upper case letter.

Second Undefined Term: Line A straight continuous arrangement of infinitely many points. It has infinite length but no thickness. It extends forever in two directions How do you name a line? AB No Arrowheads, Not a Line. B A ● ● Note: a drawing of a line has arrowheads at each end. Those arrowheads are necessary to designate that this is a “Line”.

P Third Undefined Term: Plane A plane has length and width but no thickness. It is like a flat surface that extends infinitely along its length and width. P You name a plane with a script letter. Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.

Definition: Collinear Collinear means on the same line. C B ● A ● ● Points A, B and C are collinear.

Definition: Coplanar Coplanar means on the same plane. A ● B ● C ● You name a plane with a script letter. Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.

Definition: Line Segment Line Segment A line segment consists of two points called the endpoints of the segment and the points between them. Line Segment C ● A You write a line segment as AC or CA. ● End Points Note: there are no arrowheads!

We can add segments, when we add two segments, we add their lengths. For your notebook: We can add segments, when we add two segments, we add their lengths.

I Do Example 1A: Using the Segment Addition Postulate G, F and H are three collinear points (points on the same line). G is between F and H, FG = 6, and FH = 11. Find GH. FH = FG + GH Seg. Add. Postulate 11 = 6 + GH Substitute 6 for FG and 11 for FH. – 6 –6 Subtract 6 from both sides. 5 = GH Simplify.

We Do Example 1B: Using the Segment Addition Postulate B is between A and C , AC = 24, and BC=5. Find BC.

You Do Example 1C: Using the Segment Addition Postulate Q is between K and W, KQ = 13, and QW = 12. Find KW.

I Do: Example 2A: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO Seg. Add. Postulate 17 + (3x – 5) = 5x + 2 Substitute the given values 3x + 12 = 5x + 2 Simplify. – 2 – 2 Subtract 2 from both sides. 3x + 10 = 5x Simplify. –3x –3x Subtract 3x from both sides. 10 = 2x Divide both sides by 2. 2 5 = x

I Do: Example 2A Continued M is between N and O. Find NO. NO = 5x + 2 = 5(5) + 2 Substitute 5 for x. = 27 Simplify.

E is between D and F. Find DF. We Do: Example 2B E is between D and F. Find DF.

E is between D and F. Find DE, Given: You Do: Example 2C E is between D and F. Find DE, Given: DE=3x+8 ED= 2x+2 and DF= 30

Home Practice: Worksheet titled “Segment Addition Postulate” posted at hialeahhigh.org

Geometry in Art & Nature Nature displays an infinite variety of geometric shapes and patterns that not only catch one’s eye for the beauty but for the complexity and flow. Name some examples of natural geometry.

Geometry in Art Craftsmen and artists have utilized geometry in art for centuries…really since the beginning of time. Basket weavers, woodworkers, and other craftsmen often use geometric designs to make their work more interesting and unique.

Geometry in Art Geometry is used in art to demonstrate perspective.

What did the acorn say after it grew up? Gee, I’m a tree!!!!