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Question

Construct a ∆PQR in which QR = 6 cm, PQ = 5 cm and ∠PQR = 60°. Now , construct a triangle similar to ∆PQR such that each of its sides is 35 the corresponding sides of ∆PQR.

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Solution

Steps of Construction :

Step 1. Draw a line segment QR = 6 cm.
Step 2. With Q as centre, draw an angle of 60o .
Step 3. With Q as centre and radius equal to 5 cm, draw another arc, cutting the previous arc at P.
Step 4. Join PQ and PR.
Thus, â–³ PQR is obtained .
Step 5. Below QR, draw an acute RQX.
Step 6. Along QX, mark off five points Q1, Q2, Q3, Q4, Q5, such that Q1Q2 = Q2Q3 = Q3Q4 = Q4Q5 .
Step 7. Join Q5R.
Step 8. From Q3, draw Q3S ∥ Q5R, meeting QR at S.
Step 9. From S, draw ST ∥ PR, meeting PQ at T.


Thus, △TQS is the required triangle, each of whose sides is 35 the corresponding sides of ∆PQR.

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