Construction of a Quadrilateral When Four Sides and One Diagonal Are Given
Construction ...
Question
Construction of quadrilaterals when two adjacent sides and three angles are given:
4. Construct a quadrilateral PQRS in which PQ = 4.5 cm ∠PQR=120∘,QR=3.8cm,∠QRS=100∘ and ∠QPS=60∘.
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Solution
First we draw a rough sketch of quadrilateral PQRS and write down its dimensions, as shown.(Rough Sketch) →
Steps of Construction:
Step 1: Draw PQ = 4.5 cm.
Step 2: Make ∠PQX=120∘.
Step 3: With Q as center and radius 3.8 cm, draw an arc, cutting QX at R. Join QR.
Step 4: Make ∠QRY=100∘.
Step 5: ∠QPZ=60∘ so that PZ and RY intersect each other at the point S.
Then, PQRS is the required quadrilateral.