# Constructing a Quadrilateral - Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given

## Notes

### Constructing a quadrilateral when two diagonals and three sides are given

When three sides and two diagonals were given, we first drew a triangle with the available data and then tried to locate the fourth point.

1) Construct a quadrilateral ABCD, given that BC = 4.5 cm, AD = 5.5 cm, CD = 5 cm the diagonal AC = 5.5 cm and diagonal BD = 7 cm.

Solution:

Here is the rough sketch of the quadrilateral ABCD

Step 1: Draw ∆ACD using SSS construction.

Step 2: With D as centre, draw an arc of radius 7 cm.

Step 3: With C as centre, draw an arc of radius 4.5 cm.

Step 4: Since B lies on both the arcs, B is the point intersection of the two arcs. Mark B and complete ABCD. ABCD is the required quadrilateral.

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Drawing a quadrilateral with 3 sides and 2 diagonals [00:06:53]
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