Mathematics
Using ruler and compasses only, construct a parallelogram ABCD using the following data :
AB = 6 cm, AD = 3 cm and ∠DAB = 45°. If the bisector of ∠DAB meets DC at P, prove that ∠APB is a right angle.
Answer
Steps of construction :
Draw a line segment AB = 6 cm.
With A as center draw a line AX such that ∠BAX = 45°.
From AX, cut AD = 3 cm.
With B and D as center and radii equal to 3 cm and 6 cm draw arc cutting each other at point C.
Join BC and CD.
Draw AY, the angular bisector of angle A intersecting CD at point P.
Join BP. Measure ∠APB.
On measuring ∠APB = 90°.
Hence, ABCD is the required parallelogram.
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