Mathematics
In a ΔPQR, L and M are two points on the base QR such that ∠LPQ = ∠RQP and ∠RPM = ∠RQP. Prove that
(i) ΔPQL ∼ ΔRPM.
(ii) QL × RM = PL × PM.
(iii) PQ2 = QL × QR.
Related Questions
In ΔABC, it is given that AB = 12 cm, ∠B = 90° and AC = 15 cm. If D and E are points on AB and AC respectively such that ∠AED = 90° and DE = 3 cm, prove that :
(i) ΔABC ∼ ΔAED.
(ii) ar(ΔAED) = 6 cm2.
(iii) ar(quad BCED) : ar(ΔABC) = 8 : 9.
In the given figure, ∠PQR = ∠PST = 90°, PQ = 5 cm and PS = 2 cm.
(i) Prove that ΔPQR ∼ ΔPST.
(ii) Find area of ΔPQR : Area of quadrilateral SRQT.
In the adjoining figure, the medians BD and CE of a ΔABC meet at G. Prove that :
(i) ΔEGD ∼ ΔCGB.
(ii) BG = 2 × GD.
In the adjoining figure, PQRS is a parallelogram with PQ = 15 cm and RQ = 10 cm. If L is a point on RP such that RL : PL = 2 : 3 and QL produced meets RS at M and PS produced at N, find the lengths of PN and RM.
