The Triangles chapter helps students understand geometric relationships through concepts such as similarity, proportionality, corresponding sides, and important theorems. These concepts develop logical reasoning and strengthen students’ ability to solve geometry problems. Practicing Triangles MCQs regularly helps students improve ratio calculations, theorem application, and preparation for objective questions in CBSE board exams.
A strong understanding of triangle properties makes it easier to solve geometry-based problems with accuracy and confidence. Students can practice chapter-wise MCQs and revise through Class 10 MCQs to strengthen their concepts. They can also explore CBSE Board resources and MCQs Class 10 Maths for objective practice based on the latest syllabus and exam pattern.
Topics Covered
Before solving Triangles MCQs with Answers, students should revise all important concepts carefully because many questions are theorem and ratio based. Important topics covered in this chapter :
- Similar triangles
- Congruent triangles
- Basic Proportionality Theorem
- BPT theorem
- Corresponding sides
- Corresponding angles
- Triangle similarity criteria
- AA similarity criterion
- SAS similarity criterion
- SSS similarity criterion
- Parallel line concepts
- Ratio of areas of similar triangles
- Geometric theorem-based questions
- Proportional relationships
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MCQs for Class 10 Maths Chapter 6 Triangles with Answers and Explanations
Revise important formulas and practise Triangles questions to prepare for your Class 10 Maths exam. These objective questions help students improve theorem understanding, proportional reasoning, geometry analysis, and board exam preparation skills effectively.
Q1. In two triangles, AB/DE = BC/EF and the included angles between these sides are equal. Which condition proves the triangles are similar?
A) AAA
B) SAS
C) SSS
D) RHS
Answer: B
Explanation: When two pairs of corresponding sides are proportional and the included angle is equal, the triangles are similar by the SAS similarity criterion.
Q2. If ΔABC ~ ΔDEF and AB = 6 cm, DE = 9 cm, AC = 8 cm, then DF is:
A) 10 cm
B) 12 cm
C) 14 cm
D) 16 cm
Answer: B
Explanation: Since the triangles are similar, corresponding sides are proportional.
AB/DE = AC/DF
6/9 = 8/DF
DF = 12 cm.
Q3. The ratio of the areas of two similar triangles is 25:9. The ratio of their corresponding sides is:
A) 25:9
B) 5:3
C) 3:5
D) 9:25
Answer: B
Explanation: The ratio of areas of similar triangles equals the square of the ratio of corresponding sides.
sqrt(25/9) = 5/3.
Q4. If DE || BC in ΔABC, then according to the Basic Proportionality Theorem:
A) AD/DB = AE/EC
B) AB/BC = AC/DE
C) AD/AB = EC/BC
D) AB/AC = BD/CE
Answer: A
Explanation: A line parallel to one side of a triangle divides the other two sides proportionally.
Q5. Two triangles are similar if their corresponding:
A) Sides are equal
B) Angles are supplementary
C) Angles are equal and sides are proportional
D) Sides are perpendicular
Answer: C
Explanation: Similar triangles have equal corresponding angles and proportional corresponding sides.
Q6. If the sides of two similar triangles are in the ratio 3:5, then the ratio of their perimeters is:
A) 9:25
B) 25:9
C) 3:5
D) 5:3
Answer: C
Explanation: The ratio of perimeters of similar triangles is equal to the ratio of corresponding sides.
Q7. In a right triangle, if one side is 6 cm and the hypotenuse is 10 cm, the other side is:
A) 6 cm
B) 8 cm
C) 12 cm
D) 14 cm
Answer: B
Explanation: By Pythagoras theorem:
Other side = sqrt(10^2 - 6^2)
= sqrt(100 - 36)
= sqrt(64) = 8 cm.
Q8. If ΔABC ~ ΔPQR and ∠A = 50 degree, ∠B = 60 degree, then ∠Q is:
A) 50 degree
B) 60 degree
C) 70 degree
D) 80 degree
Answer: B
Explanation: In similar triangles, corresponding angles are equal. Therefore ∠Q = ∠B = 60 degree.
Q9. The altitude of an equilateral triangle of side 8 cm is:
A) 4sqrt(3) cm
B) 8sqrt(3) cm
C) 2sqrt(3) cm
D) 6sqrt(3) cm
Answer: A
Explanation: Altitude of an equilateral triangle = (sqrt(3)/2) × side
= (sqrt(3)/2) × 8 = 4sqrt(3) cm.
Q10. If the ratio of corresponding sides of two similar triangles is 4:7, then the ratio of their areas is:
A) 4:7
B) 7:4
C) 16:49
D) 49:16
Answer: C
Explanation: Ratio of areas = square of ratio of sides
= (4/7)^2 = 16/49.
Q11. If a perpendicular is drawn from the right angle to the hypotenuse of a right triangle, then the triangles formed are:
A) Congruent
B) Similar
C) Isosceles
D) Equilateral
Answer: B
Explanation: The perpendicular divides the triangle into two triangles that are similar to each other and to the original triangle.
Q12. In ΔABC, DE || BC, AD = 3 cm, DB = 6 cm, AE = 2 cm, then EC is:
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm
Answer: C
Explanation: By BPT,
AD/DB = AE/EC
3/6 = 2/EC
EC = 4 cm.
Q13. Which of the following is always true for similar triangles?
A) Their areas are equal
B) Their perimeters are equal
C) Their corresponding angles are equal
D) Their sides are equal
Answer: C
Explanation: Similar triangles always have equal corresponding angles.
Q14. A ladder 13 m long reaches a window 12 m above the ground. The distance of the foot of the ladder from the wall is:
A) 3 m
B) 4 m
C) 5 m
D) 6 m
Answer: C
Explanation: By Pythagoras theorem:
Distance = sqrt(13^2 - 12^2)
= sqrt(169 - 144)
= sqrt(25) = 5 m.
Q15. If the sides of a triangle are 9 cm, 12 cm, and 15 cm, then the triangle is:
A) Acute-angled
B) Obtuse-angled
C) Right-angled
D) Equilateral
Answer: C
Explanation:
9^2 + 12^2 = 81 + 144 = 225
15^2 = 225
Since both are equal, the triangle is right-angled.
Q16. The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is:
A) Equal to the third side
B) Perpendicular to the third side
C) Parallel to the third side and half of it
D) Double the third side
Answer: C
Explanation: The midpoint theorem states that the joining segment is parallel to the third side and equal to half of it.
Q17. If ΔABC ~ ΔDEF and AB = 5 cm, BC = 7 cm, DE = 10 cm, then EF is:
A) 12 cm
B) 14 cm
C) 16 cm
D) 18 cm
Answer: B
Explanation:
AB/DE = BC/EF
5/10 = 7/EF
EF = 14 cm.
Q18. The ratio of the areas of two equilateral triangles having sides 5 cm and 10 cm is:
A) 1:2
B) 1:4
C) 2:1
D) 4:1
Answer: B
Explanation: Area ratio = square of side ratio
= (5/10)^2 = 1/4.
Q19. Which similarity criterion uses all three sides proportional?
A) AA
B) SAS
C) SSS
D) RHS
Answer: C
Explanation: SSS similarity criterion states that if all corresponding sides are proportional, the triangles are similar.
Q20. If one angle of a triangle is 90 degree, then the triangle is called:
A) Acute triangle
B) Obtuse triangle
C) Right triangle
D) Equilateral triangle
Answer: C
Explanation: A triangle containing one 90 degree angle is called a right triangle.
Q21. If two triangles are equiangular, then they are:
A) Congruent
B) Similar
C) Isosceles
D) Not related
Answer: B
Explanation: Equiangular triangles always satisfy the AA similarity criterion.
Q22. The hypotenuse of a right triangle is 17 cm and one side is 8 cm. The other side is:
A) 9 cm
B) 12 cm
C) 15 cm
D) 16 cm
Answer: C
Explanation: Other side = sqrt(17^2 - 8^2)
= sqrt(289 - 64)
= sqrt(225) = 15 cm.
Q23. If DE || BC and AD = 4 cm, DB = 8 cm, AE = 3 cm, then AC is:
A) 6 cm
B) 9 cm
C) 12 cm
D) 15 cm
Answer: B
Explanation: By BPT,
AD/DB = AE/EC
4/8 = 3/EC
EC = 6 cm
AC = AE + EC = 3 + 6 = 9 cm.
Q24. Which theorem is used to find the relation between sides of a right triangle?
A) Midpoint theorem
B) Pythagoras theorem
C) BPT
D) Angle bisector theorem
Answer: B
Explanation: Pythagoras theorem relates the hypotenuse and the other two sides of a right triangle.
Q25. If two triangles are similar and one pair of corresponding sides are equal, then the triangles are:
A) Congruent
B) Parallel
C) Isosceles
D) Right-angled
Answer: A
Explanation: If similar triangles have one pair of equal corresponding sides, then all corresponding sides become equal, making them congruent.
Q26. The side opposite to the right angle in a right triangle is called:
A) Median
B) Altitude
C) Hypotenuse
D) Bisector
Answer: C
Explanation: The side opposite the right angle is always the hypotenuse.
Q27. If the areas of two similar triangles are 49 sq cm and 81 sq cm, then the ratio of their corresponding sides is:
A) 7:9
B) 9:7
C) 49:81
D) 81:49
Answer: A
Explanation: Ratio of sides = sqrt(49/81) = 7/9.
Q28. In an equilateral triangle, all angles are:
A) 30 degree
B) 45 degree
C) 60 degree
D) 90 degree
Answer: C
Explanation: Every angle of an equilateral triangle measures 60 degree.
Q29. If the side of a square is doubled, then its area becomes:
A) Double
B) Triple
C) Four times
D) Eight times
Answer: C
Explanation: Area of a square depends on side^2.
If side becomes 2 times, area becomes 2^2 = 4 times.
Q30. If ΔABC ~ ΔDEF and BC/EF = 2/3, then Area(ΔABC)/Area(ΔDEF) is:
A) 2/3
B) 3/2
C) 4/9
D) 9/4
Answer: C
Explanation: Ratio of areas of similar triangles is the square of ratio of corresponding sides.
(2/3)^2 = 4/9.
Important Theorems Used in Triangles
Basic Proportionality Theorem (BPT)
This theorem states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, then those sides are divided proportionally.
BPT is one of the most important concepts in Class 10 geometry because many board questions are directly based on proportionality relationships.
AA Similarity Criterion
If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
This is one of the easiest methods to identify similar triangles quickly.
SAS Similarity Criterion
If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, then the triangles are similar.
Students should compare corresponding sides carefully while using this criterion.
SSS Similarity Criterion
If all corresponding sides of two triangles are proportional, then the triangles are similar.
This criterion mainly focuses on side-ratio comparison.
Important Instructions for Solving Triangles MCQs
- Read each geometry question carefully before selecting the answer because many MCQs are based on theorem interpretation rather than direct calculations.
- Identify corresponding sides and corresponding angles properly before applying similarity conditions.
- Check proportional relationships carefully while comparing side ratios.
- Use theorem conditions step-by-step instead of solving randomly because geometry questions require logical sequence understanding.
- Avoid calculation mistakes while simplifying ratios because small errors can change the final answer completely.
- Revise similarity criteria regularly because many objective questions directly test theorem concepts.
- Practice competency-based and case-study geometry questions regularly because the latest CBSE pattern focuses heavily on conceptual reasoning.
- Do not rush through diagram-based questions because observation mistakes are very common in geometry.
