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• Depending on the sides and diagonal lengths, establish an $$ACD$$ triangle. Based on $$SSS$$ construction.

• Make an arc, which is the length of the other diagonal (with $$D$$ as center).

• Make an arc at a specified distance of point $$C$$ (third side), on the front arc. Name the two points intersection as $$B$$.

• $$A$$, $$C$$ and $$D$$ join $$B$$. This completes both diagonals of the quadrilateral $$PQRS$$.
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.

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.

Step 3:Mark the intersection with $$O$$ and $$OG$$, $$OL$$ and $$OD$$ join.

Thus, the $$GOLD$$ is a required quadrilateral.