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CBSE · Class 10 · Mathematics

Triangles

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
In △ABC, DE ∥ BC with D on AB and E on AC. If AD = 1 cm, DB = 3 cm and AE = 2 cm, then EC is:
  1. 6 cm
  2. 2/3 cm
  3. 8 cm
  4. 7 cm
2.
△ABC ~ △PQR with AB = 8 cm, BC = 20 cm and PQ = 10 cm. Then QR is:
  1. 16 cm
  2. 20 cm
  3. 29 cm
  4. 25 cm
3.
△ABC ~ △DEF. AB = 8 cm, DE = 2 cm and the perimeter of △ABC is 84 cm. The perimeter of △DEF is:
  1. 23 cm
  2. 84 cm
  3. 21 cm
  4. 105 cm
4.
In △ABC and △DEF, AB = 6, BC = 8, CA = 9 and DE = 30, EF = 40, FD = 46 (in cm). Then:
  1. the triangles are congruent
  2. the triangles are similar by SSS
  3. the triangles are similar by AA
  4. the triangles are not similar
5.
Two triangles are similar when their corresponding angles are equal and their corresponding sides are:
  1. perpendicular
  2. in the same ratio
  3. equal
  4. parallel
6.
△ABC ~ △DEF. If ∠A = 71° and ∠B = 61°, then ∠F is:
  1. 132°
  2. 109°
  3. 48°
  4. 119°
7.
D and E are points on AB and AC of △ABC with AD = 12 cm, DB = 16 cm, AE = 3 cm and EC = 4 cm. Is DE ∥ BC?
  1. Yes, because AD = AE
  2. No, because AD/DB ≠ AE/EC
  3. Yes, because AD/DB = AE/EC
  4. It cannot be decided from lengths
8.
Assertion (A): In △ABC, DE ∥ BC with AD = 20 cm, DB = 28 cm and AE = 20 cm, so EC = 30 cm.
Reason (R): A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
In △ABC, DE ∥ BC. If AD = x + 2, DB = x + 4, AE = x − 1 and EC = x (in cm), find x.
10.
△ABC ~ △PQR. AB = 15 cm, BC = 20 cm, CA = 30 cm and PQ = 12 cm. Find QR and RP.
11.
In △ABC, ∠A = 61° and ∠B = 42°. In △DEF, ∠D = 61° and ∠E = 77°. Are the triangles similar? If so, write the similarity in the right order.
12.
D and E lie on AB and AC of △ABC with DE ∥ BC. If AD : DB = 5 : 3 and AC = 40 cm, find AE and EC.
13.
The sides of △ABC are 35 cm, 40 cm and 50 cm, and the sides of △DEF are 14 cm, 16 cm and 20 cm. Are the triangles similar? Give the criterion and the scale factor.
14.
△ABC ~ △DEF. The perimeters of △ABC and △DEF are 34 cm and 102 cm. If DE = 27 cm, find AB.
15.
In △ABC, AB = 11 cm, AC = 12 cm and ∠A = 105°. In △PQR, PQ = 22 cm, PR = 24 cm and ∠P = 125°. Are the triangles similar?
16.
ABCD is a trapezium with AB ∥ DC, and its diagonals meet at O. If AB = 6 cm, DC = 12 cm and AC = 54 cm, find AO and OC.
Section C — Word problems4 × 4 = 16 marks
17.
A vertical pole 3 m tall casts a shadow 10 m long. At the same time, a tower casts a shadow 90 m long. How tall is the tower?
18.
A girl 150 cm tall walks away from the base of a lamp post in a straight line at 1 m/s. The lamp is 275 cm above the ground. How long is the shadow after 5 seconds?
19.
Isha's eyes are 1.6 m above the ground. A mirror lies flat on the ground 1 m from Isha's feet, and in it Isha sees the top of a tree that is 5 m from the mirror. How tall is the tree?
20.
To find the width AB of a river, Meera stands at B, opposite a tree A on the far bank. Meera walks 66 m along the bank to C, then 11 m further to D, then turns at a right angle and walks away from the river until C and A are in line, at E, 9 m from D. How wide is the river?
AmbifulWorksheets
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CBSE · Class 10 · Mathematics

Answer key

Triangles · AW-10M-TRN-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(a) 6 cmAD/DB = AE/EC: 1/3 = 2/EC, so EC = 6
2(d) 25 cmQR/BC = PQ/AB = 5/4, so QR = 20 × 5/4 = 25
3(c) 21 cmperimeters are in the ratio of corresponding sides: 84 × 1/4 = 21
4(d) the triangles are not similarDE/AB = 5, EF/BC = 5, FD/CA = 46/9
5(b) in the same ratio—
6(c) 48°∠F = ∠C = 180° − 71° − 61° = 48°
7(c) Yes, because AD/DB = AE/ECAD/DB = 3/4, AE/EC = 3/4
8(d) A is false, but R is true.A is false: EC = AE × DB/AD = 28, not 30. R is true.
9x = 4AD/DB = AE/EC: (x + 2)(x) = (x + 4)(x − 1), which gives x = 4
10QR = 16 cm, RP = 24 cmscale factor PQ/AB = 4/5
11Yes, by AA: △ABC ~ △DFE∠F = 180° − 61° − 77° = 42° = ∠B, and ∠E = 77° = ∠C, so A ↔ D, B ↔ F, C ↔ E
12AE = 25 cm, EC = 15 cmAE : EC = AD : DB = 5 : 3; AE = 40 × 5/8
13Yes, by SSS; scale factor 2/514/35 = 16/40 = 20/50 = 2/5
149 cmAB/DE = 34/102, so AB = 27 × 1/3 = 9
15No: the sides are in proportion but the angles between them are not equalPQ/AB = PR/AC = 2; ∠P ≠ ∠A
16AO = 18 cm, OC = 36 cm△AOB ~ △COD (AA), so AO/OC = AB/DC = 6/12
1727 mthe sun's rays make similar triangles: height/90 = 3/10
186 mdistance walked 5 m; similar triangles: L/150 = (L + 5)/275, so L = 6
198 mthe angles at the mirror are equal, so the triangles are similar: height/5 = 1.6/1
2054 m△ABC ~ △EDC (AA): AB/DE = BC/CD, so AB = 9 × 66/11 = 54