Q. 95.0( 3 Votes )

Construct a triangle PQR with sides QR = 7 cm, PQ = 6.5 cm and PQR = 60°. Now construct another triangle, whose sides are times the corresponding sides of the given triangle.

Answer :

Steps of construction:


Step 1. Construct a line PQ of length 6.5 cm.



Step 2:


Draw angle of 60° at Q.



Step 3:


From Q draw an arc of 7 cm. The point intersects at R. Join PR.



Step 4:


Draw QX.



Step 5:


Mark the greater of i.e. 7 arcs in equal distance on QX.



Step 6:


Join Q7P and then draw a line through Q5 parallel to Q7P.



Step 7:


From R1 draw a line parallel to RQ.



Thus, R1QP1 is the required triangle.


Justification:


Since the scale factor is ,


We need to prove,



By construction,


… (1)


Also, R1Q1 is parallel to RQ.


So, this will make same angle with QP.


R1P1Q = RPQ …. (2)


Now,


In Δ R1P1Q and ΔRPQ


Q = Q (common)


R1P1Q = RPQ (from 2)


Δ R1P1Q ΔRPQ


Since corresponding sides of similar triangles are in same ratio.



From (1)



Hence construction is justified.


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