Constructing triangles
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Explainer Video
Summary
Constructing triangles
In a nutshell
Triangle constructions are performed using a ruler and either a compass or a protractor. There are three different types of triangle constructions: constructing a triangle with three given sides, constructing a triangle with two given sides and one given angle and constructing a triangle with one given side and two given angles.
Constructing a triangle with three given sides
To construct a triangle with three given sides (known as SSS), you will need a ruler and a compass.
procedure
| 1. | Draw a straight line that is as long as one of the three given lengths. |
| 2. | At each end of the line, set the compass to one of the other lengths and draw an arc about the end of the line. This will result in two arcs - each arc will represent one of the two remaining sides. |
| 3. | Draw lines from each end of the first line to the point where the two arcs intersect. This is the desired triangle. |
Constructing a triangle with two given sides and one given angle
To construct a triangle with two sides and one angle (known as SAS), you will need a ruler and a protractor.
procedure
| 1. | Draw a straight line that is as long as one of the two given lengths. |
| 2. | At one end of the line, use the protractor to measure the given angle, and use the ruler to draw a line along that angle that is as long as the remaining side. |
| 3. | Complete the triangle by drawing a line between the two open ends. |
Constructing a triangle with one given side and two given angles
To construct a triangle with one side and two angles given (known as ASA), you will again need a ruler and a protractor.
procedure
| 1. | Draw a straight line that is as long as the given length. |
| 2. | At each end of the line, use the protractor to measure the given angles. Use the ruler to draw lines along the angles at each point. There should be two lines: one at either end and each line should account for one of the two angles. |
| 3. | The triangle is completed when the two lines intersect. |
Example
Construct a triangle that has one side of , one angle of and one angle of .
Example
Construct a triangle that has two sides of lengths and and one angle of .
This is a case of SAS, so first draw a line that is long using a ruler.
Then, use a protractor to measure an angle of at one end of the line.
Using a ruler, draw a line that is long along the angle.
FInally, complete the triangle by drawing a line between the two open ends.
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Exercises
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FAQs - Frequently Asked Questions
How many different triangle constructions are there?
There are three triangle constructions: SSS, ASA and SAS.
What equipment do you need to construct a triangle?
To construct a triangle, you need a ruler and either a protractor or compass.
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