Class 10 SIMILAR TRIANGLE OBJECTIVE QUESTION

X Class 10 Triangle Case based MCQs

1 mark each

Q1. If in two triangles ABC and PQR, AB/ QR =BC/ PR= CA/ PQ , then

(A) DPQR ~ DCAB (B) DPQR ~ DABC

Q2. In ΔABC, DE II BC intersecting AB at D and AC at E, AD = 1cm, DB = 3cm, AE

= 1.5cm, AC =?

(A) 6 cm (B) 10 cm

Q3. In ΔABC, D is a point on AB and E is a point on AC, DE is joined. AD = 2, DB

= 3, AE = 3 cm, EC = 4.5. Is DE II BC?

Q4. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the

length of the side of the rhombus is

(A) 9 cm (B) 10 cm

Q5. In triangles ABC and DEF, ÐB = ÐE, ÐF = ÐC and AB = 3 DE. Then, the two

triangles are

(A) congruent but not similar (B) similar but not congruent

Q.6 The perimeters of two similar triangles ABC and PQR are respectively 36cm

and 48cm. If PQ = 12cm, then AB =

(a) 16cm (b) 20cm

Q.7 In a DABC , AD is the bisector ofÐBAC . If AB = 12cm, AC = 10cm and BD =

6cm, then DC =

(a) 22.6cm (b) 5cm

Q.8 ABC and BDE are two equilateral triangles such that D is the midpoint of BC.

Ratio of the areas of triangles ABC and BDE is

(a) 2:1 (b) 1:2 (c) 4:1 (d) 1:4

Q.9 Which False?

(a) All quadrilateral triangles are similar. (b) All circles are similar.

(c ) All isosceles triangles are similar. (d) All 30° . 60° . 90° triangles are similar.

Q.10 Two isosceles triangles have equal vertical angles and their areas are in the ratio16 :25. Then the ratios of their corresponding heights are

(a) 16 :25 (b) 256 : 625 (c) 4 : 5 (d) 3 : 5

Q.11 If DABC ~ DEDF and DABC is not similar to DDEF , then which of the following is not true?

(a) BC.EF=AC.FD (b) AB.EF=AC.DE

Q.12 Sides of two similar triangles are in the ratio of 4 : 9. Areas of these triangles are in the ratio. (a) 2 :3 (b) 4 :9 (c) 81 :16 (d) 16 : 81

Q.13 If D ABC , and DDEF are similar triangles such that Ð430 and Ð870 then ÐC =

(a) 50 (b) 60 (c) 70 (d) None of these

Q.14 Two triangles are similar but not congruent and the lengths of the sides of the first are 6cm, 11cm and 12cm. The ratio of corresponding sides of first and second triangle is 1 : 2. What is the perimeter of the second triangle:

(a) 29cm (b) 53cm (c) 58cm (d) 56cm

Q.15 For the above triangle, if AD=z, DB = z-2, AE = z+2 and EC= z -1, then z =

(a) 2 (b) 3 (c) 4 (d) 1

Q.16 In an isosceles triangle ABC, If AC = BC and AB2 = 2 AC2, then ÐC=

(a) 45 (b) 60

Q.17 In triangles ABC and DEF, ÐB = ÐE,ÐF = ÐC and AB = 3DE . Then, two triangles are

(a) congruent but not similar. (b) similar but not congruent.

(c ) neither congruent nor similar. (d) congruent as well as similar.

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