Q. 144.4( 7 Votes )

Construct a triangle PQR given that QR = 3cm, PQR = 45° and QP PR = 2 cm. Also give its justification.

Answer :

Steps of Construction:

(i) Draw the base, QR = 3 cm.




At point B, draw a ray QX, which makes RQX = 45°





(ii) Here, QP – QR = 2 cm


QP > QR


Hence, cut the line segment QD is equal to QP – QR = 2 cm from the ray QX.





(iii) Now, join RD and draw its perpendicular bisector AB, which bisects RD at M (say).


Let P be the intersection point of perpendicular bisector AB and ray QX. Join PR.



Thus, ΔPQR is the required triangle.


Justification:


Base QR and Q are drawn as given. Since, the point P lies on the perpendicular bisector of DR.


PD = PR


QD = PQ – PD


QD = QP – QR


Thus, the construction is justified.


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