Selling Geometry

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Geniuses’ for Geometry Geometry for teens.

By: Yvette Alvarran, Amber Farias, Vanessa Luna

Introduction Although it may not seem like it, geometry plays a humongous role in your life and the world around you. Our end goal of this presentation is to convince you to study, and maybe even love, geometry. Please join Geniuses’ for Geometry. Topics to be discussed:  History of Geometry  Geometry Concepts  How Geometry helps you in life  Why you should care about Geometry

More Information about Geniuses’ for Geometry Group Meeting Days: Beyonce Wasp Wednesday

Our Mascot: Harry Potter Tortoise

Euclid, Geometry Genius and Father of Geometry  Geometry is a Greek word that means “Earth Geometry”  Lived in 3rd century B.C.E.  Greek Mathematician who was influenced by Plato  Created The Elements, ultimately a geometry textbook with terms, definitions, and postulates used in math today  When Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, Euclid replied “There is no royal road to geometry."

Angles  Definition: the space between two intersecting lines or surfaces at or close to the point where they meet.  Acute Angle: Less than 90°  Right Angle: 90°  Obtuse Angle: More than 90°  Alternate Interior Angles  Alternate Exterior Angles  Consecutive Interior Angles  Vertical Angles  Corresponding Angles  Supplementary Angles

 Complementary Angles

Triangles  A three sided polygon  All three angles add up to 180°  Isosceles Triangle  Right Triangle  Equilateral Triangle  Scalene Triangle  SSS, SAS, ASA, AAS, HL Postulates can show if a triangle is congruent  SSA, AAA Postulates show triangle incongruence

Triangle Lines and Points  Concurrent Lines – 3 or more lines intersect in the same point  Concurrency – Point of intersection is those three lines  Angle Bisector – Cuts angle into 3 equal parts  Incenter – Intersection of Angle Bisector  Perpendicular Bisector – Passes through midpoint and is perpendicular  Circumcenter – Intersection of Perpendicular Bisector  Median – From vertex to midpoint on opposite side  Centroid – Intersection of Median  Altitude – “True height” of a triangle  Orthocenter – Intersection of Orthocenter

Transformations

•Translations •Reflections •Rotations

Translations • A figure that can be moved right, left, up, or down without rotating, resizing or anything else, just moving in the same distance and direction. Ex.

(x, y)  (x – 3, y – 6)

Reflections • Every point is the same distance from the central line and the reflection has the same size as the original image. Ex. Reflected over y-axis, the coordinates are (-x, y) Reflected over x-axis, the coordinates are (x, -y)

Rotations • The distance from the center to any point on the shape stays the same. Rotations are naturally counter-clockwise unless told otherwise. Ex.

Rotation of 180°

Dilations A transformation in which a polygon is enlarged or reduced by a given factor around a given center point.

Tessellations • A pattern made of identical shapes that must fit together without any gaps and should not overlap.

Why Geometry?

We will tell you why:  You need it as a basis for your math classes in high school and college  Every science and technology job uses Geometry  Geometry is used in virtually every career  Here’s a list:  Abercrombie Model, Funeral Director, Pirate, Dentist, Architects, and every engineering career will incorporate some for of geometry.

How will Geometry help me in life?

How does Geometry prepare us for the real world?

Real World Uses Translations – Architects must look at buildings to see the way they move in case they must move pieces around Reflections – Dentists use a mirror to check for cavities behind your teeth and car drivers use their car mirrors to see vehicles in their blind spots. Rotations – Computer engineers design items that must be rotated, reflected, and even translated for systems. Translations – Interior designers must look at floor patterns and make sure they all fit together.

Why should I join Geniuses’ for Geometry? All in all, Geometry has been used for thousands of years with a true and meaningful purpose. Shapes are more understandable, creativity is applied in processes, and thinking about the solution to problems comes easier when learning how to solve difficult issues. While it may seem insignificant to you now, it will most definitely come in handy whether it be a few months from now or a few decades from now. Careers in all industries will include some form of geometry and you will be grateful that you took the time out of your day to learn about math that will not only benefit you right now, but benefit the future as well.

Geometry Quotes

Life without Geometry is

Pointless