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Draw ∆PQR in which PQ = 3 cm, QR = 4 cm and RP = 5 cm. Also, draw the bisector of ∠Q.

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Steps of construction:

1. Draw a line segment PQ of length 3 cm.

2. With Q as center and radius 4 cm, draw an arc.

3. With P as center and radius 5 cm, draw an arc intersecting the previously drawn arc at R.

4. Join PR and OR to obtain the required triangle.

5. From Q, cut arcs of equal radius intersecting PQ and QR at M and N, respectively.

6. From M and N, cut arcs of equal radius intersecting at point S.

7. Join QS and extend to produce the angle bisector of angle PQR.

8. Verify that angle PQS and angle SQR are equal to 45° each.

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