Theory:

  • Depending on the sides and diagonal lengths, establish an \(ACD\) triangle. Based on \(SSS\) construction.
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  • Make an arc, which is the length of the other diagonal (with \(D\) as center).
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  • Make an arc at a specified distance of point \(C\) (third side), on the front arc. Name the two points intersection as \(B\).
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  • \(A\), \(C\) and \(D\) join \(B\). This completes both diagonals of the quadrilateral \(PQRS\).
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Example:
Construct a \(GOLD\) with quadrilateral measures as follows.
 
\(OL = 7.5 cm\), \(GL = 6 cm\), \(GD = 6 cm\), \(LD = 5 cm\), \(OD = 10 cm\).
 
Step 1: Draw Side \(GD = 6 cm\) and cut the \(G\) (\(6 cm\)) and \(D\) (\(5 cm\)) arcs above it. Mark the intersection as \(L\). \(GL\) and \(DL\) are joined.
 
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Step 2: Draw and arc from \(L\) equal to \(7.5 cm\) and from \(D\) equal to \(10 cm\), which is the length of \(OL\) and \(OD\) respectively.
 
19.PNG
 
Step 3:Mark the intersection with \(O\) and \(OG\), \(OL\) and \(OD\) join.
 
20.PNG
 
Thus, the \(GOLD\) is a required quadrilateral.