Transcript My math presentation of parallel and perpendicular lines*

Nicholas Albrecht
presents:
My math presentation
of parallel and
perpendicular lines…
And mathiness
and history
First thing of importance: history of
parallel and perpendicular lines
These were from some ancient Roman or Greek guy. His name was Euclid
(for parallel). Though there was much talk about lines that crossed in a 90
degree way, the first time it was used in math was by a French philosopher
named Cartesian.
They have been used by many unsmart people (who couldn’t figure out how
to make something like it without it… without math) to build many things
like buildings or streets or stovepipe hats in the early, undeveloped times of
the world.
Streets sometimes also have perpendicular lines, buildings to, but not really
stovepipe hats.
Parallel lines:
These lines are on the same plane and NEVER intersect.
They have the same slope
They go on forever because they are lines, so by definition they are infinite,
so if they never intersect, they are somewhat unusual (though with how
often we are using them, I am not so sure)
They are all over the place.
Perpendicular lines:
These are lines that intersect at one and only one place
Lines are generally straight, and go on forever so lines can only intersect
something once.
The lines form exact right angles.
They are also LINES, so they go on forever, just the ONE place where they
intersect forms a right angle.
Be prepared, those who proceed
may not return from the land of
the math.
The complete history of these lines
VOL1: perpendicular lines
The ancient Romans used perpendicular a lot in there architecture, they
never used it in math, the Greeks didn’t either. Cartesian was a French
Philosopher who first used these lines. Cartesian was actually the French
version of the Latinized name people gave him, his real name was Rene
Descartes. The pure Latin name was Cartesius. He was one of the big
mathematicians, like Euclid, or Aristotle, though he was French and not
Greek, Roman, or Chinese. He is very famous for the Cartesian Coordinate
system. He was born on March 31, 1596, and died on February 11, 1650, he
came into the world much later than most mathematicians, and Euclid who
invented Geometry. Cartesian was a guy who really made things easier for
the mathematicians in a place where they knew nothing for thousands of
years. Perpendicular lines were used so often by so many cultures during and
after the Fall of the Roman Empire, it is amazing that perpendicular lines had
not been “discovered” before then, but it makes the idea of Cartesian being
a real genius obvious.
The complete history of these lines
VOL2: parallel lines
This was made by Euclid, an ancient Greek Philosopher. He was alive around
the time of 300 BC. He invented the core idea of Geometry and most of the
ideas and math that goes into it. Parallel lines are one of the things that he
thought of and made an important part of Geometry. He was thinking of
things that never intersect each other, then thought of them as lines that are
infinite, and called them parallel. Thus parallel lines were born. Later came
the equations and transversal lines and the actual math that goes with it.
Most of that Euclid also came up with. It was Descartes who thought of
perpendicular lines which are the “opposite” of parallel line, so obviously
they are still a major part of parallel lines. He is an example of someone who
helped the evolution of Geometry without Euclid doing it.
Parallel lines, continued:
There are a lot of things in our world that can be called parallel, but they are
only called that because of an old Greek guy who came up with the idea for
math. Though there are many things in our world that have the
mathematical parallel lines in them, that may have happened accidentally.
People might have designed streets by only thinking about making it
straight, not about parallel lines, depending on when it happened, they may
not have even known about parallel lines. Of course, there were wagons that
would make tracks that turned into a road, that happened to be parallel, but
wagons were just made to go straight, not make lines.
Perpendicular lines continued
Boxes you get in the mail usually are designed with perpendicular lines, they
sometimes don’t look that way when they come, they have been beet and
have large dents or rips in them after there journey to you. It is a little harder
to think of perpendicular lines in our society, humans seem to like things
that “go with the flow”, rather than intersect and point at a new direction,
like perpendicular lines do to each other even though they form an orderly
shape with a right angle.
The Taipei 101 was once the tallest building,
but not anymore. It is a rare type of building.
It has a lot of perpendicular lines, though they
Were not supposed to be that way.
This is currently the tallest man made
building on this planet, you can see almost
No perpendicular lines on it, instead you
See lots of parallel lines.
A mathematical reason why Apple
stinks!!!
The Apple symbol HAS NO PARALLEL LINES!!!!!
PC logo does
Android logo does.
Maybe the apple went bad…
…?
These are obviously some more examples of parallel
lines that probably happened because some guy
wanted it to look cool (or for the thing it was representing
To work…) 
Mwhahahah!!!! Is
this presentation
38-40 min yet?
Intermission: half time show
Big marching band and some
random singer comes to the field
and sings some horrible song (with
a few exceptions)
Now is this presentation
38-40 min?
No!?!?!?!?!?!?! D***!
Transversal lines
These lines cut parallel lines usually at odd angles, but sometimes form
two or more sets of perpendicular lines. Transversal lines are still lines so
they are straight and infinite, they only intersect one line one time. As
far as we have learned, there cannot be a transversal of perpendicular
lines, there can be a line intersecting both, but not perpendicular.
Vertical angles are
congruent proof- it only
looks pretty because it
was copied from word,
and it automatically did
that
statement
<1 and <3 and vertical
<1 and <2 form a linear pair
<2 and <3 form a linear pair
<1 and <2 are supplementary
<2 and <3 form a linear pair
M<1+m<2=180
M<2+m<3=180
M<1=m<3
<1 is congruent to <3
reason
Given
Definition of linear pair
Postulate: if two angles form a
linear pair, then they are
supplementary
Definition of supplementary
angles
Algebra
Definition of congruent angles
Similarities of angles
Corresponding- 6 and 1
Alternate exterior- K and H, 6 and 3
Consecutive interior- 1 and 4
Alternate interior- 2 and4, 1 and 5
3
1
4
6
5
2
Some reasons you can use for proving
lines parallel, remember these for the
test!
Congruent corresponding angles
Congruent alternate exterior
angles
Congruent alternate interior
angles
Supplementary consecutive
interior angles.
Some important equations
Distance formula: D= (𝑥1 − 𝑥2)2 + (𝑦2 − 𝑦1)2
Equation of a line: y=mx+b
Formula for a slope: 𝑚 =
𝑦2−𝑦1
𝑥2−𝑥1
Point slope form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
Two careers that require these kinds of
lines
Civil Engineer
these engineers design buildings and roads and bridges. Though nowadays roads
are designed with parallel AND perpendicular lines purposely, the engineers are
constrained by that in their unique bridge designs. Buildings sometimes have whacky
designs, but on the inside, the hallways are normally made with parallel walls, and
intersecting halls are often perpendicular. You cannot have a road or a set of train tracks
that have both sides intersecting somewhere, because with a train, it would simply jump
off the rails and crash and explode! (would be fun to watch in a movie, but not in real like…
sometimes)
Mechanical engineer
These build and design tools and machines. Many machines need to be able to
make things that are parallel, and not skew things all up. Computer parts for example,
they must be very precise, if one thing is just slightly out of place, it wont work right (or left
because it wont work at all). A lot of parts for almost anything these days require parallel
lines (its not the 80’s anymore, we are NOT building houses like the Jetsons would have.
Mechanical engineers don’t design the 80’s houses, but they design the tools to make
them so the civil engineers can have fun designing weird stuff.). The way most people
think, you would need mathematical parallel lines and perpendicular lines in your rack of
knowledge, otherwise, you probably would have a hard time getting a job in any of these
fields.
Parallel lines really are everywhere
I have mentioned this before, but here are some more examples.
I’m sorry David, but they are even in Star Wars. And knowing Star Wars, they
probably were thinking of math at that time. However, there are very few; which is
a mathematical reason why they don’t work.
They are in many stories, historical, fantasy, and SCI-FI alike. Even horror stories sometimes do.
Even the stories them selves as in the book they are told in.
Credits:
Google (and Google Chrome)
Bing
Toshiba
Acer
…math 
Logitech
Fire Fox
Unfortunately, the math book
THE WORLD!
No help from Apple
And weather you like it or not, this was thorough and beneficial
Prepare for a study guide…