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Question
Construct a quadrilateral ABCD in which AB = 6 cm, ∠A = 60°, ∠B = 75°, AD = 4 cm and BC = 4.8 cm.
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Solution
Given:
AB = 6 cm
∠A = 60°
∠B = 75°
AD = 4 cm
BC = 4.8 cm
Step-wise calculation (Construction):
1. Draw the base:
Draw segment AB of length 6 cm.
2. Construct AD:
At A, construct ray making angle ∠DAB = 60° with AB. ...(Choose the same side of AB for both angles to get a simple quadrilateral).
On that ray mark point D so that AD = 4 cm.
3. Construct BC:
At B, construct ray making angle ∠ABC = 75° with BA. ...(Again on the same side of AB as in step 2)
On that ray, mark point C so that BC = 4.8 cm.
4. Close the quadrilateral:
Join C to D to form CD.
Join A to B already drawn, B to C and A to D already done.
The figure ABCD is now formed.
Notes
This is the standard procedure when two adjacent angles and the two adjacent sides, here AD and BC, with the included side AB, are given. Draw AB, lay off AD along the ray from A determined by ∠A, lay off BC along the ray from B determined by ∠B, then join C and D to complete the quadrilateral.
