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5 Major Geometry Concepts

A presentation by Matt Massimo elaborating on 5 important concepts in Geometry.

Matt Massimo

on 11 January 2013

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Transcript of 5 Major Geometry Concepts

Slope Identifying
Congruent Parts To identify congruent parts in a triangle you must first
know what some of the reasons are that triangles are
congruent. Here are the reasons to choose from: Converses are how you determine whether
lines are parallel or if a statement is
completely true if you are looking at
conditional statements. When using a converse
you are working on a proof where you have to
prove that the lines in the problem are parallel. The Hunt for the
5 Major Concepts
of Geometry In Geometry this semester we learned about many different concepts. Though all of these concepts are important, I am going to express which 5 I believe were some of the most important.
The 5 concepts I've selected are: The Concept of proofs The Concept of slope The Concept of congruent parts The Concept of converses The Concept Angle
Pair Relationships Proofs I believe proofs to be important because of just how much we use them and for the fact that it makes our brains look for the reasons why something does what it does. Now you might be asking "What is a proof? O.o" if you haven't taken Geometry so let me explain this concept. A proof is used to prove how and why something does what it does or to prove something that most people would just take a look at and say "This is impossible to solve..." I'm pretty sure that's what I did when I first tried to complete a proof, but now I fully understand proofs. Now to give you a better understanding here is an
example: -> This is an example of a proof, though normally there
would be a picture above to go along with the proof. Slope is an exceedingly important concept.
Slope is used to find the directions of a line on a graph. With knowing the directions you can tell whether the line has a negative slope or positive slope. The difference between these two are that negative slope goes downwards to the right and positive slope goes upwards to the right. Now you might be wondering "What if the lines are completely straight vertical or horizontal?" Well, I have the answer to that, if the line was perfectly horizontal then the line would have zero slope since it doesn't direction itself down or up. Then if a line was perfectly vertical then it would have no slope because it doesn't even go to the right at all, just plummets down. In this picture you can see the slope of the line as 1. The rise would be 1 and the run would be 1 as well. SSS- Side Side Side: All sides are congruent
SAS- Side Angle Side: 2 congruent sides with a congruent angle between them.
ASA- Angle Side Angle: 2 congruent angles with a congruent side between them.
AAS- Angle Angle Side: 2 congruent angles with a congruent side that's not between them.
HL- Hypotenuse Leg: Hypotenuses and 1 leg of
each triangle are congruent. With these reasons you can determine whether or not 2 triangles are congruent. They really make geometry a lot easier. In this picture is an example of the reason SSS (Side Side Side) that these triangles are congruent. Converses Before you can use a converse statement though you have to prove the congruency of the angles so there is something to back up the converse. The formula for slope is: "m" is the symbol for slope
y2 is a the y from one of points form graph and
x2 must be from the same point as y2 and the same rules apply for x1 and y1. Here is an example of a converse in action: Angle Pair
Relationships There are 4 angle pair relationships that are
used within geometry that we were taught this semester. Corresponding Angles: the angles that are in the same hemisphere on different lines crossed both crossed by 1 transversal.
Alternate Interior Angles: angles that are on opposite sides of the transversal between the two lines it crosses.
Consecutive Interior Angles: angles on same side of transversal between the two lines it crosses.
Alternate Exterior Angles: angles that are on opposite sides of the trasversal on the outsides of the two lines it crosses. The different corresponding angles
pairs are color coated so the 1 and 5
you can see are both light blue
since they are corresponding
angles. The color coated angles show which
angles are paired up to make
alternate interior angles. The angles are color coated to
show the other angle that it is
paired with. Consecutive Angles Alternate Interior Angles Corresponding Angles Alternate Exterior Angles The angles are color coated to show which
angles are paired up together as alternate
exterior angles. Reflection This year of geometry has been pretty good
I'd say. I did have some late work problems
(including this project) though next semester I will improve on this . During this first semester I remember at the beginning thinking that I was going to totally fail but with you teaching me Mrs. Wagner (and of course Ms. Schwab) I really understood all the concepts very well I believe. So thank you Mrs. Wagner for being a great teacher and I look forward to next semester! :)
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