Constructing an Equilateral Triangle
An equilateral triangle is one with all three sides the same length. It begins with a given line segment which is the length of each side of the desired equilateral triangle. It works because the compass width is not changed between drawing each side, guaranteeing they are all congruent (same length). It is similar to the 60 degree angle construction, because the interior angles of an equilateral triangle are . Dec 16, · Here you will be shown a short video explaining how to construct an equilateral triangle by only using a compass and ruler and no protractor. First of all dr.
This page shows how to construct draw how to make a body kit from scratch equilateral triangle inscribed in a circle with a compass and straightedge or ruler. This is the largest equilateral triangle that will fit in the circle, with each vertex touching the circle.
This is very similar to the construction of an inscribed hexagonexcept we use every other vertex instead of all six. Printable step-by-step instructions The above animation is available as a printable step-by-step instruction sheetwhich can be used for making handouts or when a computer is not available. As can be seen in Definition of a Hexagoneach side of a regular hexagon is equal to the distance from the center to any vertex.
This construction simply sets the compass width to that radius, wiith then steps that length off around the circle to create the six vertices of a hexagon. But instead of drawing a hexagon, we use every other vertex to make a triangle instead.
Since the hexagon construction effectively divided the circle into six equal arcs, by using every other point, we divide trianggle into three equal arcs instead. The three chords of these arcs form the desired equilateral triangle. Another way of thinking about it is that both the hexagon and equilateral triangle are regular polygons, one with double the number of sides of the other. The image below is the final drawing from the above animation, but with extra lines and the vertices labelled.
Home Contact About Subject Index. In the case of an inscribed equilateral triangle, we use every other point on the circle. From 2 we see that five sides are equal in length, but the last side FA was not drawn with the compasses. It was the "left over" space as we stepped around the circle and stopped at F. So we have to prove it is congruent with the other five sides. The sides are all equal radii of the circle, and from 9the included trangle are congruent.
See Test for congruence, side-angle-side 11 BDF is an equilateral triangle. This in turn satisfies the definition of an equilateral triangle. D Yo it yourself Click here for a printable worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
NOTE: Steps 1 through 7 are the same as for the construction of a hexagon inscribed in a circle. See Test for congruence, side-angle-side.
Explanation of method
OAB is an equilateral triangle: AB was drawn with compass width set to OA, and OA = OB (both radii of the circle). 4: m?AOB = 60° All interior angles of an equilateral triangle are 60°. 5: m?AOF = 60° As in (4) m?BOC, m?COD, m?DOE, m?EOF are all &60deg; Since all the central angles add to °, m?AOF = - 5(60) 6: Triangle BOA, AOF are congruent.
Last Updated: March 12, References Approved. To create this article, 55 people, some anonymous, worked to edit and improve it over time. This article has 13 testimonials from our readers, earning it our reader-approved status. This article has been viewed , times. Learn more An equilateral triangle has three sides of equal length, connected by three angles of equal width.
It can be challenging to draw a perfectly equilateral triangle by hand. However, you can use a circular object to mark out the angles. Make sure to use a ruler to get the lines straight! Continue reading to learn how to draw one. If you don't have access to a compass or a protractor, you can use an object with a circular base to trace out an arc instead. This method is essentially the same as using a compass, but you will need to be smart about it!
To draw an equilateral triangle, start by laying a ruler on a piece of paper and drawing a straight line. Next, insert a compass at an end of the line you've just drawn and put a pencil at the other. Trace a quarter circle with the pencil end of the compass moving upwards, then switch the ends of the compass around. To form the apex, draw a second arc with the pencil so it crosses over the first arc.
Finish by drawing 2 straight lines up to the apex for the triangle's sides and erasing the arcs so only the triangle can be seen. For tips on how to draw an equilateral triangle using a protractor, keep reading! Did this summary help you?
Things You'll Need. Related Articles. Article Summary. Method 1 of Draw a straight line. Lay your ruler on the paper, then trace a pencil along the straight edge. Make sure that you have plenty of room to draw all three sides!
Span the segment with your compass. Slide a pencil into your compass, and make sure that it's sharp! Put the point of your compass at one end of the segment, and set the pencil point at the other. Trace a quarter-circle arc.
Do not adjust the point of the compass, and do not change the set "width" of the tool from the compass point to the pencil point. Swing the pencil-point of the compass in a quarter-circle up and away from the line segment. Switch the compass around. Without changing the width of the compass spread, move the point of the compass to the other end. Draw a second arc. Carefully swing the pencil-point of the compass so that the new arc crosses over the first arc that you drew.
Mark the point where the two arcs cross. This is the apex the "top" point of your triangle. It should lie at the exact center of the line segment that you've drawn. You can now draw two straight lines leading to this point: one from each end of the "bottom" line segment. Finish the triangle.
Use a ruler to draw two more straight line segments: the remaining sides of the triangle. Connect each end of the original line segment to the point at which the arcs cross. Make sure that the lines are straight. To finish the job, erase the arcs that you drew so that only the triangle remains!
This way, you can start fresh with a clean shape. If you need a bigger or a smaller triangle, repeat the process but adjust the length of the original line segment. The longer the sides, the bigger the triangle! Method 2 of Choose your circular object. Use almost any cylindrical object with a circular base, like a bottle or a soup can. Try using a circular roll of tape or a CD. If you are going to substitute the arc of this object for the arc of a compass tracer, you'll need to choose an object of the right size.
In this method, each side of the equilateral triangle will be as long as the radius half the diameter of the circular object. If you use a CD as your object: imagine an equilateral triangle that fits into the top-right quadrant of a CD.
Draw the first side. It should be exactly as long as the radius of the circular object — the distance halfway across. Make sure that it is perfectly straight! If you have a ruler: simply measure the diameter of the object and draw a line that is half as long.
If you don't have a ruler: place the circular object onto a sheet of paper, then carefully trace the circumference with your pencil. Remove the object, and you should have a perfect circle. Use a straight edge to draw a line across the exact center of the circle: the point that is completely equidistant from any point around the circumference of the circle.
Use the circular object to trace an arc. Place the object over the line segment, with the edge of the circle resting at one end of the line. For accuracy, make sure that the line cleaves through the exact center of the circle. Use your pencil to trace an arc: roughly one-quarter of the way around the perimeter of the circle.
Trace another arc. Now, shift the circular object so that the edge touches the other end of the line segment. Make sure that the line segment runs through the exact center of the circle. Draw another quarter-arc that crosses the first arc at a point directly above the line segment.
This point is the apex of your triangle. Complete the triangle. Draw the remaining sides of the triangle: two more straight lines will connect the apex with the two open ends of the line segment. Now, you should have a perfectly equilateral triangle! Method 3 of Use a ruler or the straight edge of your protractor to trace a straight line segment of an appropriate length. This line segment will become the first side of your triangle, and each of the other sides will be just as long — so make sure that it's the right size!
Trace the second side. Measure out a new line segment that is equal in length to the first. Start from the vertex the point of the angle, and trace the straight edge of the protractor until you reach the next "point. Use the straight edge of your protractor to trace out the final side of the triangle. Connect the point at the end of the second line segment to the unattached end of the first line segment. You should now have an equilateral triangle. How would I draw an equilateral triangle with three lines in it forming six right angles?
Assuming you know the length of each of the three given lines and all three lines are of equal length , this is not a difficult construction. First draw any line, then draw a line segment perpendicular to the first line. On that line segment, measure off the given line length.
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