CBSE Class 10 Mathematics Triangles MCQs Set 19

Practice MCQs for Class 10 Mathematics Chapter 06 Triangles

Review structured MCQ sets for Class 10 Mathematics Chapter 06 Triangles. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Access Chapter 06 Triangles Questions and Solutions

View or download the dedicated Chapter 06 Triangles MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: In triangle ABC, D and E lie on AB and AC with DE ∥ BC. If AD = 6 cm, DB = 9 cm and AE = 8 cm, then AC equals
(a) 12 cm
(b) 14 cm
(c) 20 cm
(d) 16 cm
Show Answer & Explanation

Answer: (c) 20 cm

Explanation:
1. By the basic proportionality theorem AD/DB = AE/EC, so 6/9 = 8/EC and EC = 12 cm. Hence AC = AE + EC = 8 + 12 = 20 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 2: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD/DB = 3/4 and AC = 15 cm, then AE equals
(a) 9 cm
(b) 20/3 cm
(c) 45/7 cm
(d) 15/4 cm
Show Answer & Explanation

Answer: (c) 45/7 cm

Explanation:
1. AE/EC = AD/DB = 3/4, so AE = (3/7) × AC = 45/7 cm ≈ 6.43 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 3: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD = 4 cm, AE = 8 cm, DB = x − 4 and EC = 3x − 19, then x equals
(a) 4
(b) 8
(c) 19/3
(d) 11
Show Answer & Explanation

Answer: (d) 11

Explanation:
1. AD/DB = AE/EC gives 4/(x − 4) = 8/(3x − 19). Cross-multiplying: 12x − 76 = 8x − 32, so 4x = 44 and x = 11.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 4: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD = 8 cm, AB = 12 cm and AE = 12 cm, then CE equals
(a) 8 cm
(b) 6 cm
(c) 9 cm
(d) 18 cm
Show Answer & Explanation

Answer: (b) 6 cm

Explanation:
1. DB = 12 − 8 = 4 cm. AD/DB = AE/EC gives 8/4 = 12/EC, so EC = 6 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 5: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD = 2 cm, AB = 6 cm and AC = 9 cm, then AE equals
(a) 4.5 cm
(b) 3 cm
(c) 6 cm
(d) 2 cm
Show Answer & Explanation

Answer: (b) 3 cm

Explanation:
1. DB = 4 cm and AD/DB = 1/2 = AE/EC. So AE = (1/3) × 9 = 3 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 6: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD/BD = 4/5 and EC = 2.5 cm, then AE equals
(a) 2 cm
(b) 3.125 cm
(c) 2.5 cm
(d) 4 cm
Show Answer & Explanation

Answer: (a) 2 cm

Explanation:
1. AE/EC = AD/BD = 4/5, so AE = (4/5) × 2.5 = 2 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 7: In triangle ABC, D and E are on AB and AC with AD = 5.7 cm, DB = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm. Then
(a) DE is not parallel to BC
(b) DE ∥ BC, because both ratios equal 2/3
(c) DE ∥ BC, because AD = AE
(d) DE ∥ BC, because both ratios equal 3/5
Show Answer & Explanation

Answer: (d) DE ∥ BC, because both ratios equal 3/5

Explanation:
1. AD/DB = 5.7/9.5 = 3/5 and AE/EC = 3.3/5.5 = 3/5. The ratios are equal, so DE ∥ BC.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 8: In triangle ABC, AD bisects angle A and meets BC at D. If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, then DC equals
(a) 2.5 cm
(b) 2.1 cm
(c) 3 cm
(d) 1.5 cm
Show Answer & Explanation

Answer: (b) 2.1 cm

Explanation:
1. By the angle bisector theorem BD/DC = AB/AC, so 2.5/DC = 5/4.2 and DC = 2.5 × 4.2/5 = 2.1 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 9: In triangle ABC, AD bisects angle A and meets BC at D. If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, then AB equals
(a) 2.8 cm
(b) 4.2 cm
(c) 6.3 cm
(d) 3.5 cm
Show Answer & Explanation

Answer: (a) 2.8 cm

Explanation:
1. BD = 10 − 6 = 4 cm. AB/AC = BD/DC gives AB = 4.2 × 4/6 = 2.8 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 10: In triangle ABC, AD bisects angle A and meets BC at D. If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, then BC equals
(a) 3 cm
(b) 5.8 cm
(c) 6.2 cm
(d) 5.6 cm
Show Answer & Explanation

Answer: (b) 5.8 cm

Explanation:
1. BD/DC = AB/AC gives BD = 3 × 5.6/6 = 2.8 cm. So BC = 2.8 + 3 = 5.8 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 11: In triangle ABC, AD bisects angle A and meets BC at D. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then BD and DC are
(a) 6 cm and 6 cm
(b) 7.5 cm and 4.5 cm
(c) 8 cm and 4 cm
(d) 9 cm and 3 cm
Show Answer & Explanation

Answer: (b) 7.5 cm and 4.5 cm

Explanation:
1. BD/DC = AB/AC = 10/6 = 5/3. So BD = (5/8) × 12 = 7.5 cm and DC = (3/8) × 12 = 4.5 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 12: In triangle ABC, AE bisects the exterior angle CAD and meets BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then CE equals
(a) 12 cm
(b) 20 cm
(c) 15 cm
(d) 18 cm
Show Answer & Explanation

Answer: (d) 18 cm

Explanation:
1. For the exterior bisector EB/EC = AB/AC. With CE = x: (12 + x)/x = 10/6, so 72 + 6x = 10x and x = 18 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 13: In trapezium ABCD, AB ∥ CD and the diagonals meet at O. If OA = 3x − 19, OB = x − 4, OC = x − 3 and OD = 4, then x equals
(a) 11 only
(b) 8 or 11
(c) 8 only
(d) 4 or 19
Show Answer & Explanation

Answer: (b) 8 or 11

Explanation:
1. For AB ∥ CD, OA/OC = OB/OD, so (3x − 19)/(x − 3) = (x − 4)/4. Then 12x − 76 = x² − 7x + 12, i.e. x² − 19x + 88 = 0, giving (x − 8)(x − 11) = 0. Both values make all lengths positive.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 14: In a right triangle ABC, the right angle is at C and AC = √3 BC. Then angle ABC equals
(a) 30°
(b) 45°
(c) 75°
(d) 60°
Show Answer & Explanation

Answer: (d) 60°

Explanation:
1. tan B = AC/BC = √3, so angle ABC = 60°.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 15: Two trees 20 m and 28 m high stand on level ground and the distance between their tops is 17 m. The horizontal distance between them is
(a) 15 m
(b) 9 m
(c) 25 m
(d) 8 m
Show Answer & Explanation

Answer: (a) 15 m

Explanation:
1. The difference in heights is 28 − 20 = 8 m. By Pythagoras the horizontal distance = √(17² − 8²) = √225 = 15 m.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 16: Triangle ABC has AB = 3 cm, BC = 2 cm and CA = 2.5 cm. Triangle DEF is similar to triangle ABC with EF = 4 cm. The perimeter of triangle DEF is
(a) 7.5 cm
(b) 15 cm
(c) 12 cm
(d) 10 cm
Show Answer & Explanation

Answer: (b) 15 cm

Explanation:
1. EF corresponds to BC, so the scale factor is 4/2 = 2. The perimeter of ABC is 3 + 2 + 2.5 = 7.5 cm, so the perimeter of DEF = 2 × 7.5 = 15 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 17: In an equilateral triangle ABC, AD ⊥ BC with D on BC. Then
(a) AB² = 4AD²
(b) 3AB² = 4AD²
(c) 3AB² = 2AD²
(d) AB² = 3AD²
Show Answer & Explanation

Answer: (b) 3AB² = 4AD²

Explanation:
1. D is the mid-point of BC, so BD = AB/2. AD² = AB² − AB²/4 = 3AB²/4, hence 4AD² = 3AB².

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 18: In triangle ABC, DE ∥ BC with D on AB and E on AC. If AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm, then AE equals
(a) 1.6 cm
(b) 1.4 cm
(c) 2.1 cm
(d) 3.15 cm
Show Answer & Explanation

Answer: (b) 1.4 cm

Explanation:
1. AD/AB = AE/AC gives AE = 2.1 × 2.4/3.6 = 1.4 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 19: In triangle ABC, AD is the median through A and E is the mid-point of AD. BE produced meets AC at F. Then AF equals
(a) (1/3) AC
(b) (1/2) AC
(c) (2/3) AC
(d) (1/4) AC
Show Answer & Explanation

Answer: (a) (1/3) AC

Explanation:
1. Draw DG ∥ BF with G on AC. D is the mid-point of BC, so G is the mid-point of CF, i.e. CG = GF. In triangle ADG, E is the mid-point of AD and EF ∥ DG, so F is the mid-point of AG: AF = FG. Hence AF = FG = GC and AF = AC/3.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 20: In triangle ABC, AB = AC and AP ⊥ BC with P on BC. Then
(a) AB = AP
(b) AB > AP
(c) AB < AP
(d) AB ≤ AP
Show Answer & Explanation

Answer: (b) AB > AP

Explanation:
1. In right triangle ABP the hypotenuse AB is the longest side, so AB > AP.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 21: The ratio of corresponding sides of two similar triangles is 1 : 3. The ratio of their corresponding heights is
(a) 1 : 9
(b) 1 : 3
(c) 3 : 1
(d) 1 : 6
Show Answer & Explanation

Answer: (b) 1 : 3

Explanation:
1. Corresponding altitudes of similar triangles are in the same ratio as the corresponding sides, so the ratio is 1 : 3.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 22: The areas of two similar triangles are 49 cm² and 64 cm². The ratio of their corresponding sides is
(a) 49 : 64
(b) 7 : 8
(c) 8 : 7
(d) 7 : 9
Show Answer & Explanation

Answer: (b) 7 : 8

Explanation:
1. The ratio of areas equals the square of the ratio of sides, so the ratio of sides = √49 : √64 = 7 : 8.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 23: The areas of two similar triangles are 12 cm² and 48 cm². If the height of the smaller triangle is 2.1 cm, the corresponding height of the bigger one is
(a) 8.4 cm
(b) 6.3 cm
(c) 4.2 cm
(d) 1.05 cm
Show Answer & Explanation

Answer: (c) 4.2 cm

Explanation:
1. Ratio of areas 12 : 48 = 1 : 4, so the ratio of corresponding heights is 1 : 2. The bigger height = 2 × 2.1 = 4.2 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 24: Triangles ABC and DBC lie on the same base BC, with AL ⊥ BC and DM ⊥ BC. If AD meets BC at O, then area(ABC)/area(DBC) equals
(a) AL/OD
(b) BO/OC
(c) AO/OD
(d) AO/AD
Show Answer & Explanation

Answer: (c) AO/OD

Explanation:
1. The ratio of areas of triangles on the same base = ratio of their heights = AL/DM. Triangles ALO and DMO are similar (AA), so AL/DM = AO/OD.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 25: In triangle ABC, D and E are on AB and AC with DE ∥ BC. If AE = 2 cm, EC = 3 cm and BC = 10 cm, then DE equals
(a) 6 cm
(b) 4 cm
(c) 5 cm
(d) 3 cm
Show Answer & Explanation

Answer: (b) 4 cm

Explanation:
1. AC = 5 cm and triangle ADE ~ triangle ABC, so DE/BC = AE/AC = 2/5. Hence DE = 4 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 26: In triangle ABC, the medians BE and CF intersect at G. The line AGD meets BC at D. If GD = 1.5 cm, then AD equals
(a) 3 cm
(b) 4.5 cm
(c) 2.25 cm
(d) 6 cm
Show Answer & Explanation

Answer: (b) 4.5 cm

Explanation:
1. G is the centroid, so it divides the median AD in the ratio 2 : 1: AG = 2 GD = 3 cm. Hence AD = AG + GD = 4.5 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 27: In triangle ABC, angle ABC = 90° and BM is a median. If AB = 8 cm and BC = 6 cm, then BM equals
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 7 cm
Show Answer & Explanation

Answer: (b) 5 cm

Explanation:
1. AC = √(64 + 36) = 10 cm. In a right triangle the median to the hypotenuse is half of it, so BM = 5 cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 28: D, E and F are the mid-points of the sides BC, CA and AB of triangle ABC. If the area of triangle ABC is 24 sq. cm, the area of triangle DEF is
(a) 12 sq. cm
(b) 6 sq. cm
(c) 8 sq. cm
(d) 4 sq. cm
Show Answer & Explanation

Answer: (b) 6 sq. cm

Explanation:
1. Triangle DEF is similar to ABC with ratio 1 : 2 (mid-point theorem), so its area is 1/4 of 24 = 6 sq. cm.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

Question 29: A 25 m long ladder reaches a wall with its foot 7 m from the wall. If the top slides down 4 m, the foot of the ladder slides away from the wall by
(a) 4 m
(b) 15 m
(c) 7 m
(d) 8 m
Show Answer & Explanation

Answer: (d) 8 m

Explanation:
1. Initially the height is √(625 − 49) = 24 m. After sliding down 4 m the height is 20 m, so the foot is √(625 − 400) = 15 m from the wall. It has moved 15 − 7 = 8 m.

Teacher's Note:
1. Use the basic proportionality theorem or the angle bisector theorem, and write the ratios in the correct order.
2. Check that the answer satisfies the given ratio.

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Chapter 06 Triangles Objective Questions & Solutions for Class 10 Mathematics

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FAQs

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