Constructing triangles

Triangles and other shapes can be accurately constructed using a protractor, a pair of compasses and a ruler.

The lengths of two sides and the size of the angle in between are needed.

Make an accurate drawing of a triangle with lengths 4 cm and 6 cm with an angle of 40° in between.

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Draw the longest side using a ruler
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Use a protractor to measure the 40° angle. Put the centre of the protractor on the point A. Count from 0° from the horizontal line to 40° and put a mark at this point. This is point B
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Use a ruler to draw a line from A to B so it is 4 cm long
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Draw in the third side of the triangle from B to C

The sizes of two angles and the length of the side in between are needed.

Make an accurate drawing of a triangle with the angles 40° and 70°, with a side of length 8 cm in between.

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Draw the side using a ruler
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Use a protractor to measure the 40° angle. Put the centre of the protractor on point D. Count from 0° from the horizontal line to 40°. Put a construction mark at 40°
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Use a ruler to draw a line from D through the construction mark. Make it long
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Use a protractor to measure the 70° angle from E. Put the centre of the protractor on point E. 0° from the horizontal line to 70°. Put a mark at 70°, point F
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Use a ruler to draw a line from E to F. Make sure it crosses the 40° line

The lengths of all three sides are needed.

Make an accurate drawing of a triangle with sides of length 3 cm, 5 cm and 6 cm.

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Draw the longest side using a ruler
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Open the pair of compasses until they are 5 cm wide. Use a ruler to measure it. Draw an arc from point H above the line
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Open the pair of compasses until they are 3 cm wide. Use a ruler to measure it. Draw an arc from point J above the line
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Join the arc to the points H and J using a ruler

As with all constructions, ensure that the construction lines are not rubbed out. These show that the triangles were accurately constructed.

Loci and constructions – WJECConstructing triangles