Pythagoras and Right Triangles

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From the Pyramids to the current day, Mathematics, Measurement, and Geometry have been critical to the success of any building project.

Daniel is a Carpenter friend of Passy’s World, and has been busy making a wall frame and strengthening it using triangulation involving metal strips that are nailed to the back of the wooden frame to keep it straight and give it strength.

Image Copyright 2013 by Passy’s World of Mathematics

The diagonal metal strips and the wall frame verticals form a series of Right Angled Triangles, which give the frame strength and rigidity.

Image Copyright 2013 by Passy’s World of Mathematics

In this lesson we look at a special measuring rule for Right angled triangles.

This rule is called the “Pythagoras Theorem”, because it was invented by a Greek Mathematician whose name was Pythagoras.

The Diagonals Check for Squareness

Image Copyright 2013 by Passy’s World of Mathematics

Let’s say you have just had your favorite picture framed for a wall print.

But when you go to the shop it doesn’t look right; the frame looks crooked.

You can actually proove it is crooked by measuring the diagonals.

Image Copyright 2013 by Passy’s World of Mathematics

The green diagonal is actually slightly longer than the pink diagonal, and so we know for certain the picture frame is crooked.

THE TWO DIAGONALS OF A SQUARE OR RECTANGLE MUST BE EQUAL BECAUSE THESE SHAPES CONTAIN TWO IDENTICAL PYTHAGORAS TRIANGLES WHICH BOTH HAVE THE SAME HYPOTENUSE LENGTH.

This measuring check is a great way to check that Pictures, Doors, Windows, Cupboards, etc have been made properly, and it is regularly used by trades people and builders.

Everyone will probably be able to use this check at some stage in their lives.

Amazing History of the Pythagorean Theorem

The following five minute video gives an amazing history lesson on the Pythagoras Theorem.

The following video is about the Death of Pythagoras.

Pythagoras Rule Explained
Pythagoras was a Greek Mathematician from around 2500 BC, and developed a rule for L-shaped Right Angled Triangles.

The following diagrams show an explanation of this rule.

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Pythagoras started with a 90 degree (L-shaped) Right Triangle.

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Next he added Squares onto each side of the Triangle:

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Then he added Grid Lines to measure the Areas of these squares.

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From the values of the Squares he noticed a pattern which is now known as “The Pythagoras Theorem”.

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He then tried out this rule on many Right-Angled Triangles, and found that it always works.

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Pythagoras Theorem Example

The following example shows how to label a Right Angled Triangle and apply the Pythagoras Rule to it.

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Pythagoras and Screen Sizes

Screen sizes are measured diagonally.

This means that a 40 inch screen is actually made of a rectangle that is less than 40 inches wide.

(The screen size measurement is shown by the bright green line in the image below).

This 40 inches specified for the screen is the hypotenuse of a Right Angled Triangle, and so the bottom of screen width, (shown in blue), is part of the “L” in the triangle, and it is shorter than the diagonal 40 inches.

Image Copyright 2013 by Passy’s World of Mathematics

Pythagoras Theorem Videos

The following is a video of a Prezi presentation all about Pythagoras Triangles.

The following video shows several examples of how to work out Pythagoras type mathematics questions.

Here at Passy’s World we are big fans of the game “Halo”, so we just had to include the following video:

Equal Sides of a Square Question

These type of finding sides problems are different to the usual finding sides question.

The following video gives a good explanation of how to do this type of question.

Pythagoras Word Problems Videos

The following videos work through a couple of typical Pythagoras Word Problems

Interactive Pythagoras Online Lesson

The following online lesson from BBC Maths has video instruction as well as a question which can be done on the screen.

http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/pythagorastheoremact.shtml

Pythagoras Online Wall Wisher Resources

The following Wall Wisher page contains a page of clickable post-it notes that will take you to images, web pages, and videos all about Pythagoras Theorem.

To go to our Pythagoras Wall Wisher Resources page full screen, click the following link:

Pythagoras Millionaire Question

One other place you may use Pythagoras knowledge is on the Millionaire Game Show.

Check out the following video, where not even most of the helper audience do not know the Pythagoras 3, 4, 5 triangle either.

The video is called: “When not knowing Math can cost you \$15000″

Pythagoras Game – “Clueboxes”

Double click to open each of the nine clueboxes below.

Solve the problems inside.

Here is an example of what is inside a cluebox:

Each successful solution will supply you with a clue to use in the decoder grid below.

When you have all nine clues, click the link and enter the password.

It will take you to the treasure !

Click the following link to play this fun game:

Pythagoras Clue Boxes Game

Pythagoras Music Videos

The following video contains digital avatars singing about Pythagoras and is very entertaining.

Have a Look and Listen to this sweet jazzy tune, which shows everything you need to know and learn.

This next video is not exactly educational, but it does provide some G-Rated entertainment.

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