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How To Construct An Equilateral Triangle
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A triangle has three sides of equal length, joined by three angles of equal width. Drawing congruent triangles by hand is difficult. However, you can use a circular object to mark the angles. Be sure to use the glue to keep the lines straight! Read on to learn how to write one.
If you don’t have access to a compass or a protractor, you can use a circular object to draw an arc. This method is similar to using a compass, but you need to know!
A “wiki”, like Wikipedia, means that many of our articles are written by many authors. To create this document, 58 people, some anonymous, have edited and improved it over time. This article has been viewed 462,728 times.
Plane And Solid Geometry . And Making Sides Eb And ^f Equal. (each Will Be A Meadproportional Between Db And Bc.) (c) What Kind Of A Triangle Is Ebf? Ex. 866. Transform
To draw an equilateral triangle, start by placing the ruler on the paper and draw a straight line. Then insert the compass at the end of the line you printed, and place the pencil at the other end. Draw a quarter circle with the pencil end of the compass moving upwards, then rotate the ends of the compass. To finish the top, draw the second arc with a pencil so that it crosses over the first arc. Finally, by drawing 2 straight lines at the top for the sides of the triangle and eliminating the arcs, only the triangle is visible. For tips on drawing congruent triangles using a protractor, read on! Orange logo! An orange made to look like a glass of orange juice! Video Tutorials Video Tutorials
In the article Draw triangles on canvas, we talked about how to draw not only irregular triangles, but also how to draw congruent triangles. Congruent triangles are great for several reasons:
Actually, there is only one reason. They are tough! This becomes more apparent when looking at the flexibility of the screen. In this article, we will complicate matters and look at similar triangles in a new and deeper light.
To understand why the equilateral triangle works in such a complicated way, let’s look at the math behind it all. To start from the beginning, an equilateral triangle is a triangle with all sides of equal length:
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. Since we’re talking about a triangle here, we know that the interior angles must add up to 180 degrees. To move forward, as we are ahead of someone
Sides of equal length and interior angles of 60 degrees are characteristics of an equilateral triangle. This is the easy part. It is not easy to translate into what we decide and write. The important thing is to know the exact coordinates of the three points that make up our triangle. To help with this, let’s put our triangle in the x/y coordinate system:
This is the coordinate system you will encounter when learning about coordinate systems (perhaps in the galaxy far, far away and time far away 🛸) where values are positive to the right and above the origin (origin) and left and below are negative. This is something that needs to be explained, because in some web-related situations (*cough* Canvas *cough*), coordinate systems can be changed. Anyway, now it’s time to find the location of the three parts of our triangle.
Starting with our origin at the bottom left of our triangle, two of the three positions are easily identified:
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These two points are in a straight line. The vertical position will be 0 for both points, the horizontal position will be 0 for the first point and the length value for the second point. The third point, the top of our triangle, is more difficult to understand. Visually we know that the third point connects horizontally to the center of our triangle and vertically to the height of our triangle:
It’s a little less clear why the horizontal sign is only half the value on our side, so we’ll leave it at that for now. The task is to calculate the vertical position determined by the height of the triangle. How do we find out? The answer to this lies first in simplifying our current view of the equilateral triangle.
At this point, we see our triangle as a single entity. We can simplify our world by dividing our triangle into equal halves:
By doing this equal division, we get two triangles, with internal angles of 30 degrees, 60 degrees and 90 degrees. At this point, we can use some trigonometric concepts of our own
Construct An Equilateral Triangle Of Side 6 Cm And Mark The Incircle
It doesn’t work easily with our equilateral triangle in its healthy state. The first thing we do is label the lengths of the sides we know the values of:
The longest side of our equilateral triangle is just the same length as one side of our congruent triangle. The short side is half as long. We didn’t need math (or proper grammar) to find that the longest side of our bisector triangle is twice the length of our shortest side. So, to help calculate the height, we do another simplification. Let’s set our length to 2:
By replacing the simple length variable with something more concrete, we can calculate the height using one of the interior angles and the measure, cosine, or tangent function:
When all is said and done, the maximum value is the square root of 3:
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Yes it is. After these words and diagrams, we find the height of an equilateral triangle. The square root of three is when one side is 2. That’s a very special feature, so we need to return to variable length to be able to use what we’ve calculated in other situations:
All of this in the context of our equilateral triangle, here are our final values for the three components:
At this point, there is a basic pattern where we can draw a similar triangle of the size we want. Wow!
Now, you might be one of those people who wants the midpoint of the triangle to be the same as the origin at (0, 0) in our coordinate space. Using the previous example in the lower left of our triangle, all we have to do is rotate everything by half the vertical height and half the horizontal length to achieve ai:
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The main reason is that I like to keep the origin and midpoint of my triangle the same to implement transformations like rotation and scale (up or down). When you change an element that doesn’t really care about the origin, your changes are still applied. The fact is that they can also have the unexpected effects of changing the location. Almost always, you don’t expect this to happen. Rotating an object with the same center point and origin point reduces those space frames.
The last thing we’ll do before wrapping things up is convert what we saw earlier into some basic code snippets. In the article Draw triangles on canvas, we saw a quick and easy way to display a similar triangle on the screen. Here, we’ll expand that code and turn it into a reusable function by looking at the default, root-cause approach we saw earlier.
You can see a complete example using this function and the corresponding drawing code to fill the color and outline in the same triangle pen. The biggest difference between our code and the designs we’ve seen is the vertical positioning points. As the vertical axis of the canvas world rotates (down, up, up!), the code takes the negative of the maximum value to reflect this. If you change this code for other features, keep it
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