Question

Draw a parallelogram ABCD. such that l(DC) = 5.5 cm, m∠D = 45^ᴏ, l(AD) = 4 cm.

Answer 1

Given: DC = 5.5 cm, ∠D = 45^ᴏ, and AD = 4 cm

In parallelogram ABCD,

BC = AD = 4 cm and DC = AB = 5.5 cm (Opposite sides of parallegram are always equal)

And ∠D + ∠C = 180^ᴏ (Adjacent angles of a paralllegram is always supplementary)

or, 45^ᴏ + ∠C = 180^ᴏ

or, ∠C = 135^ᴏ

To construct: A parallelogram ABCD.



Steps of construction:

(i) Draw a line segment DC = 5.5 cm.

(ii) At point D, make an angle ∠XDC = 45^ᴏ.

(iii) With D as centre and radius of 4 cm, draw an arc to intersect the ray DX at point A.

(iv) At point C, make an angle ∠YCD = 135^ᴏ.

(v) With C as centre and radius of 4 cm, draw an arc to intersect the ray CY at point B.

(vi) Join AB.

Hence, ABCD is the required parallelogram.