InterviewSolution
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InterviewSolution
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Draw a parallelogram ABCD in which BC=5cm and angleABC=60^(@), divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD'C' similar to DeltaBDCwith scale factor (4)/(3). Draw the line segment D'A' parallel of DA, where A' lies on extended side BA. Is A'BC'D' a parallelogram ? |
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Answer» Solution :Steps of construction 1. Draw a line segment AB= 3 cm 2. Now,draw a ray BY making an acute `angleABY=60^(@)`. 3.With B as centre and radius equal to 5 cm draw an arc cut the POINT C on BY. 4. Againdraw a ray AZ making an acute `angleZAX'=60^(@)`,[`:. BY ||AZ,:.angleYBX'=ZAX'=60^(@)`] 5. With A as centre and radius equal to 5 cm draw an arc cu the point D on AZ .  6. Now, join CD and finally make a parallelogram ABCD. 7. Join BD, which is a diagonal of parallelogram ABCD. 8. From B draw any ray BX downwards making an acute `angleCBX`. 9. Locate 4 points `B_(1),B_(2),B_(3),B_(4)` on BX, such that `BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)`. 10.Join `B_(4)C` and from `B_(3)C` draw a line `B_(4)C'||B_(3)C` intersecting the extended line segment BC at C'. 11. From C' draw C'D'||CD intersecting the extended line segment BD at D'. Then, `DeltaD'BC'` is the required triangle whose sides are `(4)/(3)` of the corresponding sides of `DeltaDBC`. 12. Now draw a line segment D'A' parallel to DA, where A' lies on extended SIDE BA i.e., a ray BX'. 13. Finally, we observer that A'BC'D' is a parallelogram in which A'D'=6.5 cm A'B'=4 cm and `angleA'BD'=60^(@)` divide it into triangle BC'D' and A'BD' by the diagonal BD'. |
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