A father is rebuilding the triangular base of a garden tool shed and has kept the three measurements from his original budget plan: the base \(DE\) is 6 cm,...
Question 1 Report
A father is rebuilding the triangular base of a garden tool shed and has kept the three measurements from his original budget plan: the base \(DE\) is 6 cm, \(DF\) is 5 cm and \(EF\) is 4 cm on his scale drawing. He wants the finished model to match the shed he priced up at the timber merchant.
- Construct triangle \(DEF\) using a ruler and compasses only, showing all your construction arcs. (2)
Answer Details
A father rebuilding the triangular base of a garden tool shed has kept the three original measurements: base \(DE = 6\) cm, \(DF = 5\) cm and \(EF = 4\) cm. Triangle \(DEF\) is fixed uniquely once all three side lengths are known (the side-side-side case), so the compasses are used to find the one point F that is simultaneously \(5\) cm from D and \(4\) cm from E.
- Draw the base \(DE = 6\) cm accurately with a ruler. With the compass point on D and radius \(5\) cm, draw an arc above the line: every point on it is exactly \(5\) cm from D. [1]
- With the compass point on E and radius \(4\) cm, draw a second arc so that it crosses the first. The crossing point is exactly \(5\) cm from D and \(4\) cm from E at the same time, so it is the only possible position for F. Joining D to F and E to F with straight lines completes the triangle. [1]
Because all three sides are fixed by the construction, the two arcs must be drawn to the exact radii given, not adjusted to look right by eye.
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