Is a triangle complementary or complementary

Construct / draw a triangle

You can learn how to construct (draw) triangles here. Let's look at this:

  • A Explanation how to construct triangles.
  • Examples for drawing triangles with a set square and compass.
  • Tasks / exercises so that you can practice this yourself.
  • Some Videos for drawing triangles.
  • A Question and answer area to this topic.

Tip: If you do not understand the following content, you may have a few problems with your previous knowledge. In this case, please have a look at our triangle overview and drawing angles.

Explanation of constructing a triangle

In order to draw a triangle, you need information about it, such as the length of sides or angle sizes. Usually you need three pieces of information to clearly draw a triangle. With unambiguous it is meant that the triangles can be drawn up to congruence. Congruence? Triangles can be moved or rotated. However, the angles or side lengths do not change. If two triangles are only shifted or rotated with respect to one another, then these two triangles are congruent to one another.

In geometry, four sets of congruence are dealt with, which are also used when drawing triangles. These are:

  • Three sides are given (SSS).
  • One side, one angle and another side (SWS).
  • An angle, a side and another angle (WSW).
  • One side, a second side and an angle (SSW).

Let's look at these four cases by example.

Another hint: When we talk about the sides and lengths of a triangle, we mean the sides a, b and c as well as the angles alpha, beta and gamma. The next graphic shows you this. The graphic can also be found in our triangle overview article.

Construct (draw) triangle SSS:

The first possibility is to construct a triangle with SSS. So we gave three sides, but no angle. Example: Draw a triangle with c = 3 cm, b = 4 cm and a = 5 cm.

Solution: We first draw one of the three sides and start with c = 3 cm. We can do this with a ruler or set square. We then write a small c on this side and at the ends A and B as shown in the previous graphic.

Now we still know that b = 4 cm and a = 5 cm long. Side b is usually drawn on A and a is drawn on B. Just how do you do that? For example, how should you draw b at A if you don't know what angle size? Finally, the remaining side a must also be 5 cm long.

We solve the problem with a circle. We set this to 4 cm, as we want b = 4 cm. We pierce in A and draw a part of a circle above it:

We still need a side with 5 cm, since a = 5 cm. This side should be marked at B. Since we don't know the angle here either, we work with the compass again. We set this to 5 cm and pierce in B to draw a part of a circle again at the top.

We connect the intersection with A and B and thus have our triangle. In addition, we write a and b to it.

If you like, you can add missing angles and corner points.

Display:

Examples of constructing a triangle

In this section we look at three more examples. In order not to exceed the length of the article completely, the steps are summarized in each case.

Construct (draw) a triangle SWS:

Next we construct a triangle according to SWS. So we have a side, an angle, and another side. For example: We have given the sides b = 5 cm and c = 7 cm and the angle alpha with 30 degrees. Draw the triangle.

Solution:

  • As always, we start with c and draw in red c = 7 cm and the corner points A and B.
  • The angle alpha is marked at point A with 30 degrees.
  • The line is 5 cm long in green, because b = 5 cm.
  • We denote the end point with C.
  • We connect this with B to completely draw the triangle.

Construct (draw) triangle WSW:

The third possibility to construct a triangle is according to WSW. We have an angle, a side, and another angle. As an example we take the side length b = 4 cm and the angles alpha = 20 degrees and gamma = 40 degrees. What does the triangle look like?

Solution:

  • We first draw the side w = 4 cm in red.
  • We write A and C at the end of these pages.
  • At A we apply the angle alpha = 20 degrees.
    • First of all with a pencil, as we don't know the length of the page.
  • At B we enter the angle gamma = 40 degrees.
    • First of all with a pencil, as we don't know the length of the page.
  • At the intersection is our point B, which we connect with green and blue.

Construct (draw) a triangle SSW:

The fourth possibility is called SSW. Two sides and an angle are known. As an example, a = 5 cm and c = 6 cm. The angle gamma is 35 degrees. Draw the triangle.

Solution:

  • We draw a = 5 cm in red.
  • We draw in C and B.
  • At C we enter an angle of 35 degrees.
    • First of all with a pencil, as we don't know the length of the page.
  • The length c should be entered in blue with 6 cm.
  • But we don't know at what angle.
    • Therefore we pierce with the compass in B and draw a partial circle at 6 cm at the top.
  • The intersection is the last corner we connect.

Construct a triangle videos

Video 1

This video shows an example of how to construct a triangle. In this first video in our video article "Constructing a Triangle", the triangle is constructed from a given side and two given angles. The short form of this construction method is also called SWW.

The video shows the approach to constructing a triangle with the existing values. It starts by constructing the given page as a horizontal line. The given angle is applied to this. The finished triangle is created through parallel displacement and angular construction.

As a tool for this video, we recommend a set square, a sharp pencil and squared paper. You can also switch the video to full screen mode to see it larger. Source: Youtube.com


Next video ┬╗Show:

Draw a triangle of questions with answers

In this section we look at typical questions and answers about constructing triangles.

Q: Can you draw a triangle with less than three pieces of information (angles and sides)? Or more?

A: You can also draw triangles with less than three entries. But these are not unique; different triangles can come out of them. There can also be four or more pieces of information. In that case, however, this information must not contradict one another. For example, the three interior angles in a triangle must always be 180 degrees. No more and no less.


Q: When is this topic covered in school?

A: Drawing triangles is dealt with in 6th grade at the earliest, but in 7th grade at the latest. The topic can also be on the agenda in 8th grade.

Q: What topics should I look at next?

A: Drawing triangles is part of the geometry field. In this area we have other content available, such as this one: