Module 5 (M5) - Geometry and measures - Constructions using a ruler and a protractor

Constructions using a ruler and a protractor

It might be useful to look at M1 Properties of Angles and M1 Properties of 2D shapes.

Constructions are accurate drawings of shapes using a ruler and protractor.
From a sketch or a description, you may be asked to construct a triangle

How to construct triangles given 1 side and 2 angles

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Image caption,
What you need: ruler, protractor, pencil and paper.
Use these to construct a triangle when you know the length of 1 side and the 2 angles at each end of it.
In this case use the length 8 cm, and the two angles 40° and 50°.
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Step 1:
Draw an 8 cm line using a pencil and ruler.
Place the centre of the protractor on the end of the line and mark 40° with a dot.
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Step 2:
Use a ruler to draw a line from the end of the line through the dot and label the angle 40°.
TIP: you won't know the exact length of this new side yet so draw it a bit longer than you think you'll need. You can always extend it later.
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Step 3:
Place the protractor on the other end of the first line and mark a 50° angle up from the line with a dot.
TIP: often protractors have an inner and outer scale. Make sure you read the one that has zero on the first line.
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Step 4:
Draw a line from the end of the line through the dot so it crosses the other side. Extend the lines if you need to.
Mark this angle 50°.

You've constructed a triangle, given the length of 1 side and 2 angles.
TIP: if one of of the 2 angles is NOT at the end of the side you're given, it's easy to work out the third angle using the fact that there are 180° in a triangle.

How to construct triangles given 2 sides and 1 angle

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Step by step instructions

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Image caption,
What you need: ruler, protractor, compass, pencil and paper.
Use these to construct a triangle when you know the length of 2 sides and 1 angle
In this case use 2 side lengths of 7 cm and 8 cm and the angle 40°.
Image caption,
Step 1:
Draw a straight 8 cm line using a pencil and ruler.
Set the compass width to 7 cm. Place the compass at one end of the line and draw an arc.
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Step 2:
Centre the protractor on the same end of the line and make a dot at 40°.
From the same end, use a ruler to draw a line through the dot, crossing the arc.
Label the length 7 cm and the angle 40°.
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Step 3:
Use the ruler to join the other end of the horizontal line to the end of the side you have just drawn.

You've constructed a triangle after being told 1 angle and the length of 2 sides.

How to construct triangles given 3 sides

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Step by step instructions

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What you need: Ruler, pencil, compass, paper
Use these to construct a triangle when you know the length of all 3 sides.
In this case use the lengths 8 cm, 4 cm and 5 cm.
Image caption,
Step 1:
Draw a straight 8 cm line using a pencil and ruler.
Set the compass width to 4 cm. Place the compass at one end of the horizontal line and draw an arc.
Image caption,
Step 2:
Set the compass width to 5 cm.
Place the compass at the other end of the line and draw an arc that crosses the first arc.
Image caption,
Step 3:
Use the ruler to draw a line from the left end of the horizontal line to the point where the two arcs meet. Label the line 4 cm.
Image caption,
Step 4:
Use a ruler to join the other end of the line to the point where the two arcs meet. Label the line 5 cm.

You've constructed a triangle after being told the length of all 3 sides.