Constructing triangles: SSS, SAS, ASA

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 $7\ cm$ , one angle of $40\degree$ and one angle of $50\degree$ .

Maths; Angles and geometry; KS4 Year 10; Constructing triangles: SSS, SAS, ASA

Example

Construct a triangle that has two sides of lengths $7cm$ and $10cm$ and one angle of $40\degree$ .

This is a case of SAS, so first draw a line that is $7cm$ long using a ruler.

Maths; Angles and geometry; KS4 Year 10; Constructing triangles: SSS, SAS, ASA

Then, use a protractor to measure an angle of $40\degree$ at one end of the line.

Maths; Angles and geometry; KS4 Year 10; Constructing triangles: SSS, SAS, ASA

Using a ruler, draw a line that is $10cm$ long along the $40\degree$ angle.

Maths; Angles and geometry; KS4 Year 10; Constructing triangles: SSS, SAS, ASA

Finally, complete the triangle by drawing a line between the two open ends.

Maths; Angles and geometry; KS4 Year 10; Constructing triangles: SSS, SAS, ASA