(1) Check whether the which triangles are similar and find the value of x.
(i)
(ii)
(2) A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamppost. The girl whose height is 1.25 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamppost are in a same line, find the height of the lamp post. Solution
(3) A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower. Solution
(4) Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT × TR = ST × TQ. Solution
(5) In the adjacent figure, triangle ABC is right angled at C and DE ⊥ AB . Prove that ΔABC ∼ ΔADE and hence find the lengths of AE and DE.
(6) In the adjacent figure, ΔACB ∼ ΔAPQ . If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
(7) If figure OPRQ is a square and <MLN = 90° . Prove that (i) ΔLOP ∼ ΔQMO (ii) ΔLOP ∼ ΔRPN (iii) ΔQMO ∼ ΔRPN (iv) QR^{2} = MQ × RN
(8) If ΔABC ∼ ΔDEF such that area of ΔABC is 9cm^{2} and the area of ΔDEF is 16cm^{2} and BC = 2.1 cm. Find the length of EF. Solution
(9) Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.
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