Chapter 6: Triangles — Online MCQ Test
MATHS · CLASS 10th · Karnataka State Board
Practice Chapter 6: Triangles with a free chapter-wise online MCQ test.
This chapter covers: Similar triangles Criteria for similarity Basic proportionality theorem Pythagoras theorem Converse of Pythagoras theorem Triangle proofs Ratio of areas.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 6: Triangles — Important Questions & Answers
Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are:
- A. Equal
- B. Perpendicular
- C. Proportional
- D. Parallel
Answer: C. Proportional
Similar triangles have equal corresponding angles and proportional corresponding sides.
Similar triangles have equal corresponding angles and proportional corresponding sides.
Which similarity criterion states that two triangles are similar if their corresponding angles are equal?
- A. SSS similarity
- B. AAA similarity
- C. RHS congruence
- D. SAS congruence
Answer: B. AAA similarity
By AAA similarity, if all corresponding angles of two triangles are equal, the triangles are similar.
By AAA similarity, if all corresponding angles of two triangles are equal, the triangles are similar.
According to the Basic Proportionality Theorem, a line drawn parallel to one side of a triangle divides the other two sides in:
- A. Equal parts
- B. The same ratio
- C. Right angles
- D. A ratio of 1:2 always
Answer: B. The same ratio
The Basic Proportionality Theorem states that a line parallel to one side of a triangle divides the other two sides in the same ratio.
The Basic Proportionality Theorem states that a line parallel to one side of a triangle divides the other two sides in the same ratio.
In a right-angled triangle, the square of the hypotenuse is equal to:
- A. The sum of the squares of the other two sides
- B. The difference of the squares of the other two sides
- C. Twice the product of the other two sides
- D. The sum of all three sides
Answer: A. The sum of the squares of the other two sides
By Pythagoras theorem, hypotenuse² = perpendicular² + base².
By Pythagoras theorem, hypotenuse² = perpendicular² + base².
In triangle ABC, D lies on AB and E lies on AC. If DE is parallel to BC, AD = 3 cm, DB = 4 cm and AE = 6 cm, then EC is:
- A. 6 cm
- B. 7 cm
- C. 8 cm
- D. 10 cm
Answer: C. 8 cm
By BPT, AD/DB = AE/EC. So 3/4 = 6/EC, giving EC = 8 cm.
By BPT, AD/DB = AE/EC. So 3/4 = 6/EC, giving EC = 8 cm.
If triangle ABC is similar to triangle DEF and AB:DE = 2:3, then ar(ABC):ar(DEF) is:
- A. 2:3
- B. 3:2
- C. 4:9
- D. 9:4
Answer: C. 4:9
The ratio of areas of similar triangles is the square of the ratio of corresponding sides, so it is 2²:3² = 4:9.
The ratio of areas of similar triangles is the square of the ratio of corresponding sides, so it is 2²:3² = 4:9.
Two vertical poles cast shadows at the same time. A 6 m pole casts a 4 m shadow. If another pole casts an 18 m shadow, its height is:
- A. 12 m
- B. 18 m
- C. 24 m
- D. 27 m
Answer: D. 27 m
The pole and its shadow form similar right triangles. Therefore height/shadow = 6/4, so height = 18 × 6/4 = 27 m.
The pole and its shadow form similar right triangles. Therefore height/shadow = 6/4, so height = 18 × 6/4 = 27 m.
Triangle ABC is similar to triangle DEF. If AB = 6 cm, BC = 8 cm, CA = 10 cm and DE = 9 cm, where AB corresponds to DE, then the perimeter of triangle DEF is:
- A. 27 cm
- B. 30 cm
- C. 36 cm
- D. 40 cm
Answer: C. 36 cm
The scale factor is DE/AB = 9/6 = 3/2. So EF = 12 cm and FD = 15 cm; perimeter = 9 + 12 + 15 = 36 cm.
The scale factor is DE/AB = 9/6 = 3/2. So EF = 12 cm and FD = 15 cm; perimeter = 9 + 12 + 15 = 36 cm.
In triangle ABC, P lies on AB and Q lies on AC such that PQ is parallel to BC. If AP:PB = 2:3 and the area of trapezium PBCQ is 84 cm², then the area of triangle APQ is:
- A. 12 cm²
- B. 16 cm²
- C. 20 cm²
- D. 24 cm²
Answer: B. 16 cm²
AP/AB = 2/5, so ar(APQ)/ar(ABC) = 4/25. The trapezium area is 21/25 of ar(ABC), so ar(ABC) = 100 cm² and ar(APQ) = 16 cm².
AP/AB = 2/5, so ar(APQ)/ar(ABC) = 4/25. The trapezium area is 21/25 of ar(ABC), so ar(ABC) = 100 cm² and ar(APQ) = 16 cm².
Two similar triangles have areas in the ratio 25:49. If the difference between a pair of corresponding medians is 6 cm, then the smaller median is:
- A. 12 cm
- B. 15 cm
- C. 18 cm
- D. 21 cm
Answer: B. 15 cm
The ratio of corresponding medians is the square root of the area ratio, i.e., 5:7. The difference of 2 parts is 6 cm, so 1 part is 3 cm and the smaller median is 15 cm.
The ratio of corresponding medians is the square root of the area ratio, i.e., 5:7. The difference of 2 parts is 6 cm, so 1 part is 3 cm and the smaller median is 15 cm.