![Page 1: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/1.jpg)
Welcome!
![Page 2: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/2.jpg)
![Page 3: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/3.jpg)
Building Blocks of Geometry
Because without geometry…life is pointless
![Page 4: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/4.jpg)
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.
![Page 5: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/5.jpg)
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)
![Page 6: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/6.jpg)
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.
![Page 7: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/7.jpg)
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.
![Page 8: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/8.jpg)
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
![Page 9: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/9.jpg)
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
![Page 10: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/10.jpg)
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.
![Page 11: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/11.jpg)
First Undefined Term:
Point The most basic building block of geometry. It has no size. It has only location.
A
●
Note: you name a point with a single upper case letter.
You represent a point with a dot
![Page 12: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/12.jpg)
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
AB
●●
Note: a drawing of a line has arrowheads at each end. Those arrowheads are necessary to designate that this is a “Line”.
No Arrowheads, Not a Line.
How do you name a line?
AB
![Page 13: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/13.jpg)
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.
Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.
You name a plane with a script letter.
P
![Page 14: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/14.jpg)
Definition:
Collinear Collinear means on the same line.
Points A, B and C are collinear.
AB
C
●●
●
![Page 15: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/15.jpg)
Definition:
Coplanar Coplanar means on the same plane.
Note: Represent a plane with a four-sided figure, like a tilted piece of paper drawn in perspective.
You name a plane with a script letter.
A
BC●
●
●
![Page 16: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/16.jpg)
![Page 17: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/17.jpg)
We can add segments, when we add two segments, we add their lengths.
![Page 18: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/18.jpg)
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.
5 = GH
FH = FG + GH Seg. Add. Postulate
11 = 6 + GH – 6 –6
Substitute 6 for FG and 11 for FH.Subtract 6 from both sides.
Simplify.
![Page 19: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/19.jpg)
We Do Example 1B: Using the Segment Addition Postulate
B is between A and C , AC = 24, and BC=5. Find AB.
![Page 20: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/20.jpg)
You Do Example 1C: Using the Segment Addition Postulate
Q is between K and W, KQ = 13, and QW = 12. Find KW.
![Page 21: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/21.jpg)
I Do: Example 2A: Using the Segment Addition Postulate
M is between N and O.
Find NO.
10 = 2x
NM + MO = NO Seg. Add. Postulate
17 + (3x – 5) = 5x + 2
– 2 – 2
Substitute the given values
Subtract 2 from both sides.Simplify.3x + 12 = 5x + 2
3x + 10 = 5x –3x –3x
2 2 5 = x
Simplify.Subtract 3x from both sides.
Divide both sides by 2.
![Page 22: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/22.jpg)
I Do: Example 2A Continued
M is between N and O.
Find NO.
NO = 5x + 2
Substitute 5 for x.
Simplify.= 27
= 5(5) + 2
![Page 23: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/23.jpg)
E is between D and F. Find DF.
We Do: Example 2B
![Page 24: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/24.jpg)
E is between D and F. Find DE, Given:
DE=3x+8 EF= 2x+2 and DF= 30
You Do: Example 2C
![Page 25: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/25.jpg)
Home Practice:
Worksheet titled “Segment Addition Postulate” posted at hialeahhigh.org
![Page 26: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/26.jpg)
Geometry in Nature
![Page 27: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/27.jpg)
![Page 28: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/28.jpg)
![Page 29: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/29.jpg)
![Page 30: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/30.jpg)
![Page 31: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/31.jpg)
Geometry in Video Games
![Page 32: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/32.jpg)
Geometry in Basketball
![Page 33: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/33.jpg)
Geometry in Art
![Page 34: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/34.jpg)
What did the acorn say after it grew up?
Gee, I’m a tree!!!!
![Page 35: Welcome!. Building Blocks of Geometry Because without geometry… life is pointless](https://reader031.vdocuments.mx/reader031/viewer/2022013115/56649e695503460f94b65e94/html5/thumbnails/35.jpg)
Sometime yesterday…