Practice Sheet – 07

CLASS
Similarity
07

PQR S T PQ PR
1. Which of the following is a true statement

I. Triangle PST is similar to triangle PQR.

(a) Two similar triangles are always congurent
PST, PQR

(b) Two similar trinagles have equal areas. 1

II. ST = (QR)
2

(c) Two triangle are similar if their corresponding III. ST is parallel to QR./ST, QR
sides are proportional. (a) Only I and II (b) Only II and III
(c) Only I and III (d) All I, II and III
(d) Two polygons are similar if their correspond- SSC CGL 2021 (Tier–I)

ing sides are proportional. 5.  ABC is similar to  PQR. AB = 4 cm, BC = 8 cm

and AC = 10 cm. If QR = 16 cm, then what is the
SSC CGL 2018 (Tier–I)
area of  PQR?
2. ABC is a triangle in which  ABC = 90º. BD is per-  ABC,  PQR AB = 4cm, BC = 8cm and
pendicular to AC. which of the following is TRUE? AC = 10 cm QR = 16 cm  PQR
ABC  ABC = 90º BD, AC
(a) 2 231 cm2 (b) 4 231 cm2
I. Triangle BAD is similar to triangle CBD.
(c) 4 462 cm2 (d) 7 231 cm2
BAD, CBD
SSC CHSL 2022 (Tier-1)
II. Triangle BAD is similar to triangle CAB.
6. In  ABC. D is a point on side BC such that
BAD, CAB
 ADC =  BAC. If CA = 12 cm, CD = 8 cm, then CB
III. Triangle CBD, is similar to triangle CAB.
(in cm) = ?
CBD, CAB
 ABC BC D  ADC
(a) Only I (b) Only II and III
=  BAC CA = 12 cm, CD = 8 cm CB (
(c) Only I and III (d) All I, II and III
)
SSC CGL 2021 (Tier–I)

3. In  ABC and  DEF, if  A = 50º,  B = 70º, (a) 18 (b) 12 (c) 15 (d) 10

SSC CGL 2022 (Tier–II)
 C = 60º,  D = 60º,  E = 70º, and  F = 50º, then
7. In  ABC, D is a point on side BC such that  ADC
 ABC  DEF  A = 50º,  B = 70º,
=  BAC. If CA = 12cm, CB = 8 cm, then CD is
 C = 60º,  D = 60º,  E = 70º,  F = 50º
equal to:
(a)  ABC   FED (b)  ABC   DFE  ABC BC D  ADC =
(c)  ABC   EDF (d)  ABC   DEF  BAC CA = 12 CB = 8 CD
SSC MTS 2018

4. PQR is a triangle. S and T are the midpoints of the

sides PQ and PR respectively. Which of the follow- (a) 18cm (b) 16cm (c) 12cm (d) 15cm
SSC MTS 2021
ing is TRUE?

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8.  ABC, AB = 20 cm, BC = 7 cm and CA = 15 cm. QR 14
Sid e BC i s pro duced to D such t hat  PY = 18 PQ
XY 9
 DAB   DCA. DC is qual to :
 ABC AB = 20 BC = 7 CA = 15
P
BC D
 DAB   DCA DC Y
(a) 10 cm (b) 9 cm (c) 7 cm (d) 8 cm X 105°
SSC CGL 2020 (Tier–II)
75° 60°
9. In the given figure, ABCD is a rectangle and P is a
point on DC such that BC = 24 cm, DP = 10 cm and Q R
CD = 15 cm. If AP produced intersects BC produced (a) 28 (b) 18 (c) 21 (d) 24
at Q, then the length of AQ. SSC CGL 2019 (Tier–II)
13. ABCD is a square. Draw a triangle QBC on side BC
ABCD DC P
considering BC as base and draw a triangle PAC
BC = 24 DP = 10 CD = 15 on AC as its base such that QBC  PAC
AP BC Q
Area of QBC
AQ then Area of  PAC is equal to :

A D ABCD BC BC QBC
AC PAC
P
QBC
QBC  PAC
PAC
B Q
C
2 1 1 2
(a) (b) (c) (d)
(a) 24 cm (b) 26 cm (c) 39 cm (d) 35 cm 3 3 2 1
SSC CGL 2020 (Tier–II) SSC CGL 2018 (Tier–I)

10. Triangle ABC is similar to triangle PQR and AB : 14. In equilateral  ABC, D and E are points on the
PQ= 2 : 3. AD is median to the side BC in triangle side AB and AC, respectively, such that AD = CE.
ABC and PS is the median to side QR in triangle BE and CD intersect at F. The measure (in
PQR. What is the value of (BD/QS)²? degrees) of  CFB is:
ABC, PQR AB : PQ= 2 : 3  ABC D E AB AC
AD, ABC BC PS,
AD = CE BE CD F
PQR QR (BD/QS)²
 CFB
3 4 2 4 (a) 120° (b) 125° (c) 135° (d) 105°
(a) (b) (c) (d)
5 9 3 7 SSC CGL 2020 (Tier–II)
SSC CGL 2019 (Tier–II)
15. In  ABC, D and E are the points on AB and AC
11. XYZ is a triangle. If the medians ZL and YM
intersect each other at G, then (Area of  GLM : respectively such that AD × AC = AB × AE. If  ADE
Area of  XYZ) is: =  ACB + 30° and  ABC = 78°, then  A = ?

XYZ ZL YM  ABC AB AC D E
G,  GLM  XYZ AD × AC = AB × AE  ADE =  ACB + 30°
 ABC = 78° A = ?
(a) 1 : 14 (b) 1 : 12 (c) 1 : 11 (d) 1 : 10 (a) 68° (b) 48° (c) 56° (d) 54°
SSC CHSL 2020 SSC CGL 2021 (Tier–II)

QR 14 16. In a square ABCD, diagonals AC and BD interest

12. In the given figure, if  and PY = 18 cm, at O. The angle bisector of  CAB meets BD and
XY 9
then what is the value (in cm) of PQ? BC at F and G, respectively. OF : CG is equal to:

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 ABCD AC BD, O
 CAB BD BC F
G OF : CG

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

SSC CGL 2020 (Tier–II)

Answer Key

1. (c) 6. (a) 11. (b)

2. (d) 7. (a) 12. (a)
3. (a) 8. (d) 13. (c)
4. (d) 9. (c) 14. (a)
5. (d) 10. (d) 15. (d)
16. (a)

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