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Watch this video for a quick example of the power of real world triangles.

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Why Are Triangles Stronger Than Squares?

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In 2 to 5 sentences at the bottom of your assignment, tell me what you learned from this lesson? Did something about triangles in the real world stand out to you? Did you find the math we use to find triangle sides and angles easy and handy for real life situations. Did you learn something about a future career on its use of triangles that you had not realized before now?

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You may think: "Why did I have to do this assignment?"
Well, triangles are all around us. People have made careers on dealing with and manipulating triangles to be used for technology and building.
Click on this length to read the importance of Triangles.

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Triangle is some of the simplest shapes there are. But this doesn't mean that they are not important!

A triangle is a three-sided polygon and comes in a variety of flavours. Some are to do with the length of the triangle's sides: equilateral — where all the sides (and all the angles) are the same size; isosceles — where two of the sides (and two of the angles) are the same size; and scalene — where none of the sides (or angles) are the same. The angles inside the triangle are also important. The sum of the angles is always 180°. You can have acute triangles, where all the angles are less than 90° and obtuse triangles, where one of the angles is greater than 90°. And of course you can get right-angled triangles — one of the most important mathematical shapes inspiring Pythagoras' Theorem and trigonometry.

But triangles aren't just mathematically significant, they are also fundamental to the way we build our environments, both physical and virtual. Triangles are special because they are exceptionally strong. Out of all the two-dimensional shapes we can make out of straight struts of metal, only a triangle is rigid. All other shapes can be deformed with a simple push if the shape is hinged at the corners (for example, a rectangle can be pushed over into a parallelogram). But not the trusty triangle, which explains its ubiquitous use in construction, from pylons to bracing.

Triangles are also special because they are the simplest polygon — a common approach to a tricky geometrical problem, such as analysing a complex surface, is to approximate it by a mesh of triangles. This approach is also used in the real world to achieve some of the exotic shapes we now see in modern architecture, such as the curved shape of 30 St Mary's Axe, aka the Gherkin, or the canopy over the courtyard in the British Museum.

The method of triangulation is also vital in building our virtual world. The CGI characters we see in film and on TV are usually approximated by an incredibly fine mesh of triangles, as this makes it easier to digitally store and manipulate them.

Triangles — the simple shapes that make our mathematical, physical and digital worlds go round.

Further reading

You can read more about triangles in the following articles on Plus magazine:

Pylon of the month explores triangle strength;

Perfect buildings: The maths of modern architecture explores the role of triangles in architecture;

It's all in the detail explores the role of triangles in the virtual world.

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Triangle is some of the simplest shapes there are. But this doesn’t mean that they are not important!

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Careers that Deal with Triangles Daily: Carpenter

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Careers that Deal with Triangles Daily: Carpenter

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A Carpenter who builds anything from the tiniest of birdhouses to massive mansions uses triangles all the time. To be a Carpenter you will need to know how to use math to correctly build structures out of wood and stone.
Click on this Link to see what math the Carpenter uses. It looks pretty similar does it not?

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The Pythagorean theorem is used extensively in carpentry and construction. Almost every carpentry project involves some combination of squares and triangles.

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. The square of side A plus the square of side B equals the square of side C.

A ² + B ² = C ²

The square of one side of a right triangle equals the square of the hypotenuse minus the square of the other side. The length of the square of side A equals the square of side C minus the square of side B.

A ² = C ² - B ²

If this sounds complicated, consider the 3-4-5 rule of a right-triangle. It is the best way to square two walls. Here's how it works - if one side of a right-triangle is three feet and the other side is four feet and the hypotenuse (or long side of the triangle) is five feet, then angle 'A' is 90 degrees (see diagram at right). If you want to square something larger, you can use proportions of this same formula, such as6-8-10.

5 ² = 4 ² + 3 ² or 10 ² = 8 ² + 6 ²

How to calculate the square feet of a triangle

The area of a triangle is equal to one-half the product of the base and height.

A = .5 x (B x H)

How to calculate the area of a rectangle

To calculate the area of a rectangle, simply multiply the length of side 1 by the length of side 2.

A = S ₁ x S ₂

How to calculate the area of a trapezoid

To calculate area of a trapezoid, multiply its height by one-half the sum of the parallel sides.

A = .5 x (L ₁ + L ₂) x H

Calculate area of a circle

To calculate the area of a circle, multiply the circumference by one-half the radius.

A = C x .5(R)

Or, multiply the radius ² by 3.1416 (pi).

A = 3.1416 x R ²

How to calculate circumference of a circle

To calculate the circumference of a circle, multiply the diameter by 3.1416 (pi).

C = 3.1416 x D

How to calculate the volume of a cylinder

To calculate the volume of a cylinder, multiply the radius squared x 3.1416 (pi) x the height of the cylinder.

V = 3.1416 x R ² x H

What next?

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Carpentry Math - Learn the basic math formulas used in carpentry

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The Pythagorean theorem is used extensively in carpentry and construction. Almost every carpentry project involves some combination of squares and triangles. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

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Careers that Deal with Triangles Daily: Engineer

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Careers that Deal with Triangles Daily: Engineer

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Have you ever seen a bridge that looked like this one? They are everywhere. Many Engineers have used our known knowledge of triangles to make bridges like this one that are safe for us to cross.
Click on this length that further explains this type of Engineering with Triangles.

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Click on the Image and you will have a clear visual of the worksheet. You may take a sheet of notebook paper and redraw these triangles and work each problem out just like our previous Videos demonstrated. Take your time and you can always reflect back to the videos.

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Right Triangle Trig Missing Sides and ...

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Right Triangle Trig Missing Sides and Read more about kuta, software, nearest, triangle, worksheet and trig.

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This video goes over our knowledge on types of Triangles and how to identify them and how to find missing angle lengths.

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This Video demonstrates how to think about triangles and how to solve for missing side lengths.

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This video will help you with how to draw straight lines for your triangles in the assignment.

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Construct a triangle with ruler, compass and protractor

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7.G.A.2 Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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Students will construct triangles and identify missing sides and angles. Students will recreate the triangles from the assignment onto their own notebook or graph paper to find the missing angles and sides. All students will be able to complete this project with 90% accuracy.

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Challenge: Can you identify all the Triangles in this image?

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Challenge: Can you identify all the Triangles in this image?

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Once you have your answer, click on the link and scroll down to the second heading to find if your answer is correct.

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How many triangles are there?

Calling all brain teaser aficionados: This triangle trick (and no, it's not an optical illusion) is sure to baffle even the most astute of brains for at least a few minutes.

Kumar Ankit, an engineering student from India, designed and posted this geometric puzzle to Quora, challenging users to find all the hidden triangles in this image (nothing goes super-viral like a controversial shape). You're going to have to really exercise that eye for detail (and a thorough concept of geometry) to solve this visual riddle. Don't get discouraged if you're more right-brained than left-these visual brain teasers and rebus puzzles are probably right up your alley. If picture puzzles are more of your thing, see if you can find the hidden objects in these pictures.

How Many Triangles Do You See?

The answer is lucky number 24-25 if you want to get fussy.

At first glance, the image seems to be a simple illustration with multiple shapes. Now here's the catch-count how many triangles are in the drawing. People are scratching their heads at the different numbers they are coming up with (something similar happens with this viral duck riddle).

If you're completely stumped, we'll give you a hint: The trick lies in factoring multiple smaller triangles into becoming a bigger triangle.

Got an answer? If you did the math and your answer was 24, congratulations, you're in the majority. Most people on Quora agreed that the answer is 24, with each row containing six triangles. If you're into shapes, also try to figure out how many squares are in this image.

However, if you really want to get technical, the truly "correct" answer is 25. The 25th triangle is hidden in the "A" in the artist's signature in the right-hand corner. An even more nitpicking Quora user noted there was another triangle in the image if you count the word "triangles." Less than 1% of people can ace this shapes brainteaser (though we bet the aforementioned eagle-eyed user is among that statistic).

Math expert Martin Silvertant posted a very helpful graphic on the site walking through how to locate the pictorial triangles and provided a logical explanation as to how you can stretch the number to 26 of them. "A triangle is a mathematical idea rather than something real; physical triangles are by definition not geometrically perfect, but approximations of triangles. In other words, both the pictorial triangles and the words referring to triangles are referents to the concept of a triangle," said Silvertant. If that was way too easy for you to figure out, these logic puzzles will keep you guessing.

If you're really getting into the debate and want to hash out (or defend) your answer, check out the entire for different users' mathematical methods-and then check out these Quora discussion math puzzles for more brain busters. If you're up for another challenge, try these brain teasers that will leave you stumped.

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How Many Triangles Do You See in This Puzzle?

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How many triangles are there? Calling all brain teaser aficionados: This triangle trick (and no, it's not an optical illusion) is sure to baffle even the most astute of brains for at least a few minutes.

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If you got the Challenge correct you could potentially win $1 Million Dollars by knowing Triangles. In the hit show "Survivor" on CBS, the players are given an even harder triangle puzzle and if they got it correct, they had a huge advantage in being one step closer in winning the Million Dollar Prize!!