In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. Pythagoras theorem ppt is related to Grade 8 and focuses on standards 8.G.6. This Lumos presentation viewer page not only allows you to view and download Pythagoras theorem ppt but also view questions, videos, apps, books and other resources related to 8.G.6.
- Pythagoras Theorem Presentation Examples
- Pythagoras Theorem Presentation Definition
- Pythagoras Theorem Presentation Worksheets
- Pythagoras Theorem Worksheet
- Pythagorean Theorem Presentation - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. This is a lesson that I created to teach my 8th grade students about the Pythagorean Theorem.
- This is a PowerPoint math or maths presentation on The Theorem of Pythagoras. We start by looking at some of characters included in Raphael's fresco 'The School of Athens' from the Vatican Museum. We see Plato and Aristotle as the central characters and then show others including Socrates, Euclid and Pythagoras.
Pythagoras
Over 2000 years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°) ..
.. and squares are made on each of the three sides, ..
.. then the biggest square has the exact same area as the other two squares put together!
It is called 'Pythagoras' Theorem' and can be written in one short equation:
a2 + b2 = c2
Note:
- c is the longest side of the triangle
- a and b are the other two sides
Definition
The longest side of the triangle is called the 'hypotenuse', so the formal definition is:
In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
Sure .. ?
Let's see if it really works using an example.
Example: A '3,4,5' triangle has a right angle in it.
Let's check if the areas are the same: 32 + 42 = 52 Calculating this becomes: 9 + 16 = 25 It works .. like Magic! |
![Theorem Theorem](/uploads/1/2/6/4/126461255/514494686.gif)
Why Is This Useful?
If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)
How Do I Use it?
Write it down as an equation:
Then we use algebra to find any missing value, as in these examples:
Example: Solve this triangle
Put in what we know:52 + 122 = c2
25+144=169:169 = c2
Square root of both sides:c = √169
You can also read about Squares and Square Roots to find out why √169 = 13
Download the latest version of Age of Empires III for Mac - Strategy game of conquest and war. Read 7 user reviews of Age of Empires III on MacUpdate. Age of Empires III: Definitive Edition — Hotfix 4087 Good day, explorers! Today’s update includes several critical fixes to the most prevalent crashes identified over the past week—all of which have been packaged up, tested, and released as soon as possible to mitigate the disruptions to your play.
Download Age of Empires III Update for Mac to update this real-time strategy game set in the Age of Discovery. How To Download Age Of Empires Online For Mac Download Age Of Empires 2 For Mac Aug 24, 2011 A new patch specifically targeting Mac gamers has been released for Age of Empires III, the third installment in the popular real-time-strategy (RTS) franchise, portraying the colonization of the. Age of Empires II HD Game for MacOSX Free Download. In Empire II: HD, fans, both original and new players will fall in love with Empire II. Discover all the first-player strategy from Kings and Expansion Conquerors, choose thousands of years of history, and go online to compete with other Steam players in their quest for dominance in the world.
![Buy age of empires 2 for mac online download](/uploads/1/2/6/4/126461255/342504948.jpg)
Example: Solve this triangle.
Put in what we know:92 + b2 = 152
Take 81 from both sides: 81 − 81 + b2 = 225 − 81
Square root of both sides:b = √144
Example: What is the diagonal distance across a square of size 1?
Put in what we know:12 + 12 = c2
1+1=2: 2 = c2
Square root of both sides:c = √2
It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled.
Example: Does this triangle have a Right Angle?
Does a2 + b2 = c2 ?
- a2 + b2 = 102 + 242 = 100 + 576 = 676
- c2 = 262 = 676
They are equal, so ..
Yes, it does have a Right Angle!
Example: Does an 8, 15, 16 triangle have a Right Angle?
Does 82 + 152 = 162 ?
- 82 + 152 = 64 + 225 = 289,
- but 162 = 256
So, NO, it does not have a Right Angle
Example: Does this triangle have a Right Angle?
Does a2 + b2 = c2 ?
Does 3 + 5 = 8 ?
Yes, it does!
So this is a right-angled triangle
And You Can Prove The Theorem Yourself !
Get paper pen and scissors, then using the following animation as a guide:
- Draw a right angled triangle on the paper, leaving plenty of space.
- Draw a square along the hypotenuse (the longest side)
- Draw the same sized square on the other side of the hypotenuse
- Draw lines as shown on the animation, like this:
- Cut out the shapes
- Arrange them so that you can prove that the big square has the same area as the two squares on the other sides
Another, Amazingly Simple, Proof
Pythagoras Theorem Presentation Examples
Here is one of the oldest proofs that the square on the long side has the same area as the other squares.
Watch the animation, and pay attention when the triangles start sliding around. Mac music visualizer.
You may want to watch the animation a few times to understand what is happening.
The purple triangle is the important one.
becomes |
We also have a proof by adding up the areas.
Pythagoras Theorem Presentation Definition
Historical Note: while we call it Pythagoras' Theorem, it was also known by Indian, Greek, Chinese and Babylonian mathematicians well before he lived ! |
Pythagoras Theorem Presentation Worksheets
Pythagoras Theorem Worksheet
Activity: Pythagoras' Theorem
Activity: A Walk in the Desert
Activity: A Walk in the Desert