# Practice on Similarity

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In this section we provide you practice on similarity

1. A man goes 12 m due south and then 35 due west. How far is he from the starting point?
(a) 47 m (b) 23.5 m (c) 23 m (d) 37 m

2. The height of an equilateral triangle having each side 12 m, is
(a) 6√2cm (b) 6√3cm cm (c) 3√6cm cm (d) 6√6cm cm

3. In δABC, DE∥BC so that AD = cm, AE = cm, DB = cm and EC = . Then we have:
(a) =3 (b) = 5 (c) = 4 (d) = 2.5

4. ΔABC ∼ ΔDEF such that AB = 9.1 cm and DE = 6.5 cm. if the perimeter of ∆DEF is 25 cm, what is the perimeter of ∆ABC?
(a) 35 cm (b) 28 cm (c) 42 cm (d) 40 cm

5. It is given that ΔABC ∼ ΔPQR andBC/QR = 2/3, then
ar(ΔPQR) / ar(ΔABC)

(a)2/3 (b)3/2 (c) 4/9 (d) 9/4

6. In ΔABC, DE ∥ BC and AD/DB = 3/5 . If AC = 4.8 cm, find the length of AE.

7. In ΔABC, LM∥AB. If AL = , AC = 2x, BM = x – 2, BC = 2x + 3, find the value of x.

8. In ΔABC, DE ∥ BC, AD = 2 cm, BD = 2.5 cm, AE = 3.2 cm and DE = 4 cm. Find AC and BC.

9. In ΔABC, AD⊥ BC and AD2 = BD.CD Prove that ∠BAC = 90°.

10. In an isosceles ∆ABC, with AB = AC, BD is perpendicular from B to the side AC. Prove that BD2 - CD2 = 2CD.AD.

11. ABCD is a trapezium in which AB || DC and AB = 2DC. Determine the ratio of the areas of ΔAOB and ΔCOD.

12. P is the mid point of BC and Q is the mid point of AP. If BQ when produced meets AC at R, prove that RA = 1/3 CA.

13. Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

14. ABC is a right triangle, right angled at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and
AD = 3√5 /2 cm, find the length of CE.

15. From a point O in the interior of a ∆ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that

(a) AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2

(b) AF2 + BD2 + CE2 = AE2 + CD2 + BF2

Criteria for Similarity

AAA Similarity
AA Similarity
SSS Similarity
SAS similarity
Practice on Similarity

From Practice on Similarity to Criteria for Similarity of Triangles

Similarity of Triangles