Are you confused by the theorems and principles in Chapter 6, ‘Triangles,’ of Class 10 Maths? Do concepts like the similarity of triangles and their properties seem overwhelming? Don’t worry!
We have the perfect resource to guide you: the Class 10 Maths Chapter 6 Triangles MCQs Quiz. This free online test will help you strengthen your grasp of this chapter and understand the pattern of questions asked in the exam. Let’s boost your board exam preparation with this effective Triangles quiz!
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Triangles MCQs Quiz
Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..
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Q: 1/15
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Q1: The corresponding sides of two similar triangles are in the ratio 3:5. What will be the ratio of their areas?
A: 3:5
B: 9:25
C: 27:125
D: 6:10
Explanation: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. The ratio of sides is 3:5, so the ratio of areas = (3/5)² = 9/25 = 9:25.
Q2: Two triangles are similar if:
A: Their corresponding angles are equal
B: Their corresponding sides are proportional
C: Their corresponding angles are equal and corresponding sides are proportional
D: Their areas are equal
Explanation: Two triangles are said to be similar if (i) their corresponding angles are equal, and (ii) their corresponding sides are proportional. Only one condition is not sufficient; both must be satisfied.
Q3: In triangles ABC and DEF, if \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} \), then which of the following statements is true?
Explanation: When the three corresponding sides of two triangles are proportional, then the triangles are similar according to the SSS (Side-Side-Side) similarity criterion.
Q4: In \( \triangle ABC \), DE || BC where D and E are points on sides AB and AC respectively. If AD = 3 cm, DB = 6 cm and AE = 4 cm, what is the length of EC?
A: 2 cm
B: 4 cm
C: 6 cm
D: 8 cm
Explanation: According to the Basic Proportionality Theorem (BPT), if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio. Here, DE || BC, so \( \frac{AD}{DB} = \frac{AE}{EC} \Rightarrow \frac{3}{6} = \frac{4}{EC} \Rightarrow EC = \frac{4 \times 6}{3} = 8 \) cm.
Q5: The perimeters of two similar triangles are 25 cm and 15 cm. If one side of the first triangle is 9 cm, what is the corresponding side of the second triangle?
A: 5.4 cm
B: 3.6 cm
C: 5.4 cm
D: 6.5 cm
Explanation: The perimeters of similar triangles are in the same ratio as their corresponding sides. Ratio of perimeters = 25:15 = 5:3. First side = 9 cm, let the second side = x cm. Then, \( \frac{9}{x} = \frac{5}{3} \Rightarrow x = \frac{9 \times 3}{5} = \frac{27}{5} = 5.4 \) cm.
Q6: A girl 90 cm tall is walking away from the base of a lamp-post at a speed of 1.2 m/s. The lamp is 3.6 m above the ground. What will be the length of her shadow after 4 seconds?
A: 1.2 m
B: 1.6 m
C: 1.8 m
D: 2.0 m
Explanation: Distance covered by the girl in 4 seconds = speed × time = 1.2 × 4 = 4.8 m. Let the length of the shadow be y m. By similarity of triangles: \( \frac{3.6}{4.8 + y} = \frac{0.9}{y} \). Solving: \( 3.6y = 0.9(4.8 + y) \) ⇒ \(3.6y = 4.32 + 0.9y \) ⇒ \(2.7y = 4.32 \) ⇒ \( y = \frac{4.32}{2.7} = 1.6 m \).
Q7: The areas of two similar triangles are 64 sq cm and 121 sq cm respectively. If one side of the first triangle is 8 cm, what is the corresponding side of the second triangle?
A: 11 cm
B: 9.5 cm
C: 10 cm
D: 12 cm
Explanation: The ratio of the areas of two similar triangles = (Ratio of their sides)². Ratio of areas = 64:121 = (8/11)². Thus, the ratio of sides = 8:11. The first side is 8 cm, so the second side = \( \frac{11}{8} \times 8 = 11 \) cm.
Q8: If two triangles have their corresponding angles equal, then they are definitely ______.
A: Congruent
B: Similar
C: Isosceles
D: Right-angled
Explanation: If two triangles have their corresponding angles equal, then they are similar by the AA (Angle-Angle) similarity criterion. For congruence, the sides must be equal as well.
Q9: In \( \triangle PQR \), S and T are points on sides PQ and PR respectively such that ST || QR. If PS = 4 cm, SQ = 6 cm and PT = 5 cm, what is the length of TR?
A: 6.5 cm
B: 7 cm
C: 7.5 cm
D: 8 cm
Explanation: By the Basic Proportionality Theorem (BPT), \( \frac{PS}{SQ} = \frac{PT}{TR} \). Given values: \( \frac{4}{6} = \frac{5}{TR} \Rightarrow TR = \frac{5 \times 6}{4} = \frac{30}{4} = 7.5 \) cm.
Q10: To divide a given line segment in a given ratio, we use the ______ theorem.
A: Basic Proportionality Theorem
B: Pythagoras Theorem
C: Mid-point Theorem
D: Angle Bisector Theorem
Explanation: To divide a line segment in a given ratio, we use the Basic Proportionality Theorem (or Thales Theorem), which states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides in the same ratio.
Q11: In two triangles, if one pair of angles is equal, the third angle will automatically be equal because the sum of angles of a triangle is ______.
A: 90°
B: 120°
C: 360°
D: 180°
Explanation: The sum of the three interior angles of any triangle is 180°. If two corresponding angles of two triangles are equal, then the third angle will also be equal (by subtracting from 180°).
Q12: A line drawn parallel to one side of a triangle intersecting the other two sides at two distinct points, the triangle formed is ______ to the original triangle.
A: Congruent
B: Similar
C: Isosceles
D: Right-angled
Explanation: According to the converse of the Basic Proportionality Theorem, if a line intersects two sides of a triangle at distinct points and is parallel to the third side, then it divides the two sides in the same ratio and the smaller triangle formed is similar to the original triangle.
Q13: In \( \triangle ABC \) and \( \triangle DEF \), \( \angle A = \angle D \) and \( \angle B = \angle E \). AB = 5 cm, BC = 8 cm and DE = 7.5 cm. What is the length of EF?
A: 10 cm
B: 11 cm
C: 12 cm
D: 13 cm
Explanation: Since \( \angle A = \angle D \) and \( \angle B = \angle E \), the triangles are similar by AA criterion: \( \triangle ABC \sim \triangle DEF \). Therefore, \( \frac{AB}{DE} = \frac{BC}{EF} \Rightarrow \frac{5}{7.5} = \frac{8}{EF} \Rightarrow EF = \frac{8 \times 7.5}{5} = \frac{60}{5} = 12 \) cm.
Q14: If two triangles are right-angled and have one acute angle equal, then they will be similar by the ______ criterion.
A: SSS
B: SAS
C: RHS
D: AA
Explanation: Both triangles are right-angled, so each has one angle (90°) equal. It is given that one acute angle is also equal. Thus, due to the equality of two angles, they are similar by the AA (Angle-Angle) criterion.
Q15: In triangle ABC, AD is the bisector of angle A meeting side BC at D. If AB = 10 cm, AC = 14 cm and BC = 12 cm, what is the length of BD?
A: 4 cm
B: 5 cm
C: 6 cm
D: 7 cm
Explanation: By the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the ratio of the adjacent sides. Hence, \( \frac{BD}{DC} = \frac{AB}{AC} = \frac{10}{14} = \frac{5}{7} \). Let BD = 5x, DC = 7x. Then BD + DC = BC = 12 cm ⇒ 5x + 7x = 12 ⇒ 12x = 12 ⇒ x = 1. Therefore, BD = 5x = 5 cm.
Quiz Results
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Class 10 Maths Chapter 6 Triangles MCQs Quiz
Chapter 6, ‘Triangles,’ is centered on the concept of similarity of triangles. In this chapter, you will learn when two triangles are considered similar and the various conditions (AA, SSS, SAS) for proving their similarity. You will understand the Basic Proportionality Theorem (BPT) or Thales’ theorem, which relates to a line drawn parallel to one side of a triangle. Additionally, you will study the ratio of the areas of similar triangles and the Pythagoras Theorem and its converse. These concepts are fundamental for the CBSE Class 10 Maths Quiz and your board exams.
Conclusion
Success in a geometry chapter like ‘Triangles’ comes from deeply understanding the theorems and practicing questions based on them. Our Class 10 Maths Chapter 6 Triangles MCQs Quiz is designed to give your practice a new direction. This quiz helps you strengthen your grip on key topics like the Similarity of Triangles and the Basic Proportionality Theorem, providing practice in solving questions accurately under time pressure. By solving these objective questions, you can assess your preparation and gain the confidence to excel in your board exams. Start this Free Online Maths Quiz for Class 10 now!
FAQs on Chapter 6 Triangles MCQs
1. Question: How many marks from the chapter Triangles are asked in the board exam? Answer: This chapter typically carries 7-9 marks in the CBSE board exam, including MCQs, short answer, and long answer (proof-based) questions.
2. Question: What are the most important theorems in this chapter? Answer: The most important theorems are the Basic Proportionality Theorem (BPT), the criteria for similarity of triangles, and the Pythagoras Theorem and its converse.
3. Question: Is this Triangles quiz based on the NCERT syllabus? Answer: Yes, our Triangles Class 10 quiz is fully based on the NCERT curriculum and the CBSE syllabus.
4. Question: What are similar triangles? Answer: Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional.
5. Question: What is the Basic Proportionality Theorem? Answer: The theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
6. Question: Is this online quiz free? Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.
7. Question: How should I prepare this chapter for the board exam? Answer: First, understand all the theorems and their proofs. Then, solve the examples and exercise questions from the NCERT book. Finally, test your skills with our Triangles Online Test.
8. Question: What is the ratio of the areas of two similar triangles? Answer: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
9. Question: What is the Pythagoras Theorem? Answer: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
10. Question: What is the benefit of taking this online quiz? Answer: This quiz helps you improve time management, check the accuracy of your concepts, and understand the exam pattern, which boosts your confidence and leads to better performance.
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