Q. 54.1( 252 Votes )

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60°. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC.

Answer :

Given in Δ ABC,

  • Length of side BC = 6 cm.
  • Length of side AB = 5 cm.
  • ∠ ABC = 60°.

Steps of Construction:

  1. Draw a line segment BC of length 6 cm.

2. With B as center, draw a line which makes an angle of 60° with BC.

Construction of 60° angle at B:
a. With B as centre and with some convenient radius draw an arc which cuts the line BC at D.


b. With D as radius and with same radius (in step a), draw another arc which cuts the previous arc at E.


c. Join BE. The line BE makes an angle 60° with BC.

  1. Again with B as centre and with radius of 5 cm, draw an arc which intersects the line BE at point A.


4. Join AC. This is the required triangle.

 

  1. Now, from B, draw a ray BX which makes an acute angle on the opposite side of the vertex A.

6. With B as center, mark four points B1, B2, B3 and B4 on BX such that they are equidistant. i.e. BB1 = B1B2 = B2B3 = B3B4.


7. Join B4C and then draw a line from B3 parallel to B4C which meets the line BC at P.


8. From P, draw a line parallel to AC and meets the line AB at Q. Thus ΔBPQ is the required triangle.

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