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__:

- 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.

- 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.

- 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 B

_{1}, B

_{2}, B

_{3}and B

_{4}on BX such that they are equidistant. i.e. BB

_{1}= B

_{1}B

_{2}= B

_{2}B

_{3}= B

_{3}B

_{4}.

7. Join B

_{4}C and then draw a line from B

_{3}parallel to B

_{4}C 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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