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 B1, B2, B3, B4 on BX where BB1 = B1B2 = B2B3 = B3B4
11. Join B4C and from B3C construct a line B4C’ || B3C 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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