Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and angABC 60 deg divide it into triangles BCD and ABD by the diagonal BD Construct the triangle BD'C' similar to traiBDC with scale factor Draw the line segment D'A' parallel to DA where A' lies on

Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and $ABC= 60^{\circ}$ , divide it into triangles BCD and ABD
by the diagonal BD. Construct the triangle BD'C' similar to DBDC with scale factor $\frac{4}{3}$ . Draw the line segment D'A' parallel to DA where A' lies on the extended side BA. Is A'BC'D' a parallelogram?

Answers (1)

Solution

Steps of construction
1. Draw, A-line AB = 3 cm
2 Draw a ray by making $\angle ABP= 60^{\circ}$
3.   Taking B as the centre and radius equal to 5 cm. Draw an arc which cuts BP at point C
4.   Again draw ray AX making $\angle {Q}'AX= 60^{\circ}$
5.   With A as the centre and radius equal to 5 cm draw an arc which cuts AX at point D
6.   Join C and D Here ABCD is a parallelogram
7.   Join BD , BD is a diagonal of parallelogram ABCD
8.   From B draw a ray BQ with any acute angle at point B i.e., $\angle CBQ$ is an acute angle
9.   Locate 4 points $B_{1},B_{2},B_{3},B_{4}$ on BQ with equal distance.
10. Join $B_{3}C$ and from   $B_{4},{C}'$ parallel to $B_{3}C$ which intersect at point ${C}'$
11. From point   ${C}'$ draw a line ${C}'{D}'$ which is parallel to CD
12. Now draw a line segment ${D}'{A}'$ parallel to the DA
Note: Here ${A}',{C}'$ and ${D}'$ are the extended sides.
13.   ${A}'B{C}'{D}'$ is a parallelogram in which ${A}'{D}'= 6\cdot 5\, cm$ and ${A}'{B}= 4\, cm$ and $< {A}'B{D}'= 60^{\circ}$ divide it into triangles $B{C}'{D}'$ and ${A}'{BD}'$ by the diagonal ${BD}'$