**Worksheet on Similar Triangles for Grade 10 :**

Here we are going to see some practice problems based on the concept similar triangles.

(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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