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MathidiaMathematics Academy
Angles and constructions
Lesson 60 of 75
Review

Construct triangles

Objective. Create triangles from side and angle information.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Constructing a triangle means drawing it accurately using given information such as side lengths and angles, with a ruler, protractor and compasses. To construct a triangle from three side lengths (SSS), draw one side first, then use compasses set to the other two lengths to find where the third vertex lies. To construct using two sides and the included angle (SAS), draw one side, use a protractor to mark the angle at one end, then draw the second side along that angle. Checking the final triangle's measurements against the original information confirms an accurate construction.

Worked example

Describe how to construct a triangle with sides of 6 cm and 4 cm and an included angle of 50° between them.

Diagram of a triangle
  1. 1Draw a straight line 6 cm long using a ruler, labelling the ends A and B.
  2. 2Use a protractor at point A to mark an angle of 50° from the line AB.
  3. 3Draw a line from A along this angle measuring exactly 4 cm, labelling the end C.
  4. 4Join points B and C with a ruler to complete the triangle.

Answer: Triangle ABC constructed with AB=6 cm, AC=4 cm and angle A=50°

Concept mastery

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Practice

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Common mistake. Pupils sometimes forget to use the given angle at the correct vertex when constructing with SAS, drawing the angle at the wrong end of the line. Always check which vertex the given angle belongs to before drawing.

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