Construct a Triangle From Given Measures

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Goal

Construct a triangle when the given measures tell you enough information about the sides and/or angles.

Read the measures carefully. Identify what is given: side lengths, angle measures, or both.
Draw a clear starting segment if needed. If a side length is given, begin with that side as a base and label its endpoints.
Use the appropriate construction tool.
- For a side length, mark the required distance with a compass or ruler.
- For an angle, draw a ray and copy the given angle with a protractor or compass construction.
Locate the third vertex. Use the remaining measure(s) to find where the two constraints meet.
Connect the points. Draw the triangle’s sides carefully and label the vertices.

Make sure each given measure appears in the finished triangle.
Check that the sides and angles are consistent with the information provided.
If more than one placement seems possible, verify that you used the correct orientation and that the triangle is valid.

A good construction is neat and exact: the triangle should match the given measures, not just look close.