Subjects
Grades
Constructing a Triangle
Concept sheet | Mathematics
Secondary
1-2
There are three ways to construct a triangle depending on the information given.
It is important to know the properties of triangles to understand the constraints that must be respected.
Method Using Three Side Measurements
Use a compass and a ruler to draw a triangle when the measurements of its three sides are known.
-
Using a ruler, draw a line segment with the same measurement as one side of the triangle.
-
Open the compass to a size that matches the other side of the triangle. Place the sharp point of the compass on one end of the line segment drawn in step 1. Draw a circle.
-
Open the compass to a size that matches the third side of the triangle. Place the sharp point of the compass on the other end of the line segment drawn in step 1. Draw a circle.
-
To form the triangle, draw two lines connecting the endpoints of the line segment drawn in step 1 to one of the two intersection points of the circles drawn in steps 2 and 3.
Refer to the following example.
Draw a triangle with sides that measure |4\:\text{cm},| |5\:\text{cm}| and |7\:\text{cm}.|
 |
 |
 |
 |
Method Using Measurements of One Side and the Two Angles Situated at its Endpoints
Using a protractor and a ruler, draw a triangle when the measurements of one of its sides and two of its angles are known. See the following method.
-
Using a ruler, draw a line segment with a measurement corresponding to the known side of the triangle.
-
Using a protractor, draw one of the known angles of the triangle at one end of the line segment drawn in step 1.
-
Again using the protractor, draw the other known angle of the triangle at the other end of the line segment drawn in step 1.
-
Trace the angle formed by the lines drawn in steps 2 and 3 to form the complete triangle.
See the following for a more detailed example.
Imagine drawing a triangle where one side measures |5\:\text{cm}| and the measurement of the two angles are |30°| and |70°.| Follow these steps.
|
 |
 |
 |
Method Using Measurements of an Angle and the Two Sides That Form it
Using a protractor and a ruler, draw a triangle when the measurements of one of its angles and the two sides that form it are known. Follow these steps.
-
Using a ruler, draw a line segment that has the same measurement as a known side of the triangle.
-
Using a protractor, trace a line to draw the known angle of the triangle at one end of the line segment drawn in step 1.
-
Using the ruler again, identify the measurement of the second side of the triangle on the line drawn in step 2.
-
Join the ends of the first and second line segments.