Welcome Building Blocks of Geometry Because without geometry
Welcome!
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. A You represent a point with a dot Note: you name a point with a single upper case letter.
Second Undefined Term: Line How do you name a line? AB A Note: a drawing of a line has arrowheads at each end. Those arrowheads are necessary to designate that this is a “Line”. A straight continuous arrangement of infinitely many points. It has infinite length but no thickness. It extends forever in two directions B No Arrowheads, Not a Line.
Third Undefined Term: Plane You name a plane with a script letter. A plane has length and width but no thickness. It is like a flat surface that extends infinitely along its length and width. P Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.
Definition: Collinear means on the same line. A ● Points A, B and C are collinear. B ● C ●
Definition: Coplanar means on the same plane. A ● C ● You name a plane with a script letter. B ● Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.
We can add segments, when we add two segments, we add their lengths.
I Do Example 1 A: 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 11 = 6 + GH – 6 5 = GH Seg. Add. Postulate Substitute 6 for FG and 11 for FH. Subtract 6 from both sides. Simplify.
We Do Example 1 B: Using the Segment Addition Postulate B is between A and C , AC = 24, and BC=5. Find AB.
You Do Example 1 C: Using the Segment Addition Postulate Q is between K and W, KQ = 13, and QW = 12. Find KW.
I Do: Example 2 A: Using the Segment Addition Postulate M is between N and O. Find NO. NM + MO = NO 17 + (3 x – 5) = 5 x + 2 3 x + 12 = 5 x + 2 – 2 3 x + 10 = 5 x – 3 x 10 = 2 x 2 2 5=x Seg. Add. Postulate Substitute the given values Simplify. Subtract 2 from both sides. Simplify. Subtract 3 x from both sides. Divide both sides by 2.
I Do: Example 2 A Continued M is between N and O. Find NO. NO = 5 x + 2 = 5(5) + 2 Substitute 5 for x. = 27 Simplify.
We Do: Example 2 B E is between D and F. Find DF.
You Do: Example 2 C E is between D and F. Find DE, Given: DE=3 x+8 EF= 2 x+2 and DF= 30
Home Practice: Worksheet titled “Segment Addition Postulate” posted at hialeahhigh. org
Geometry in Nature
Geometry in Video Games
Geometry in Basketball
Geometry in Art
What did the acorn say after it grew up? Gee, I’m a tree!!!!
Sometime yesterday…
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