# Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor 4/3. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram

**Solution:**

Steps of Construction

1. Construct a line AB = 3 cm

2. Construct a ray BY which makes an __acute angle__ ∠ABY = 60°

3. With B as centre and 5 cm as radius, construct an arc which cuts the point C on BY

4. Construct a ray AZ which makes ∠ZAX’ = 60° as BY || AZ and ∠YBX’ = ∠ZAX’ = 60°

5. With A as centre and 5 cm as __radius__, construct an arc which cuts the point D on AZ

6. Join CD

7. So we get a __parallelogram__ ABCD

8. Join BD which is the __diagonal__ of parallelogram ABCD

9. Construct a ray BX downwards which makes an acute angle ∠CBX

10. Now locate 4 points B_{1}, B_{2}, B_{3}, B_{4} on BX where BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4}

11. Join B_{4}C and from B_{3}C construct a line B_{4}C’ || B_{3}C which intersects the extended line segment BC at C’

12. Construct C’D’||CD which intersects the extended line segment BD at D’. ∆D’BC’ is the required triangle whose sides are 4/3 of the __corresponding sides__ of ∆DBC

13. Construct a line segment D’A’||DA where A’ lies on the extended side BA

14. We see that A’BC’D’ is a parallelogram where A’D’ = 6.5 cm, A’B = 4 cm and ∠A’BD’ = 60°

15. Divide it into triangles A’BD’ and BC’D’ by the diagonal BD’.

Therefore, A’BC’D’ is a parallelogram.

**✦ Try This: **Draw a parallelogram ABCD in which BC = 3 cm, AB = 4 cm and ∠ABC = 30°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor 1/4. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 2**

## Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor 4/3. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram

**Summary:**

A parallelogram ABCD is drawn with BC = 5 cm, AB = 3 cm and ∠ABC = 60°. It is divided into triangles BCD and ABD by the diagonal BD. The triangle BD' C' similar to ∆BDC with scale factor 4/3 is constructed. The line segment D'A' parallel to DA where A' lies on the extended side BA is drawn. Yes, A’BC’D’ is a parallelogram

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