CBSE Class 10 Mathematics Chapter 6 Triangles — 20 MCQs with Answers

Similar Triangles — Fundamental Concepts and Notation

• If ΔABC ~ ΔDEF with similarity ratio 2:3, then AB/DE = BC/EF = CA/FD = 2/3, and every linear measurement scales by the same factor.
• Symbol '~' denotes similarity; '≅' denotes congruence. Confusing the two in an MCQ loses you the mark.
• The scale factor (or ratio of similitude) k is always written as the ratio of a side of the first triangle to the corresponding side of the second.

Basic Proportionality Theorem (Thales Theorem) and Its Converse

• Standard notation: In ΔABC, if DE ∥ BC and D is on AB, E is on AC, then AD/DB = AE/EC (dividing AB and AC internally).
• The converse is a powerful tool for proving lines parallel without angle measures, useful in construction-based MCQs.
• BPT does not apply if the line intersects extensions of the sides outside the triangle; that scenario uses the external division version, rarely tested at Class 10.

Criteria for Similarity — AA, SSS, and SAS

• AA is the quickest criterion in most geometry problems because angles are easier to find (via parallel lines, isosceles triangles, or angle sum) than side lengths.
• SSS similarity is tested with numerical ratios; always simplify ratios before comparing to avoid arithmetic mistakes.
• SAS similarity demands the angle between the two proportional sides; a common trap is giving two sides and a non-included angle, which proves nothing.

Areas of Similar Triangles and the k² Ratio

• If the side ratio is 3:4, the area ratio is 9:16. If the area ratio is given as 25:36, the side ratio is 5:6.
• This theorem holds for any pair of corresponding linear measurements—medians, altitudes, angle bisectors—all scale by k, so their squares give area comparisons.
• In problems involving similar triangles inscribed in circles or similar polygons, always check whether the question asks for linear or area ratio.

Application Problems — Heights, Shadows, and Indirect Measurement

• When two objects and their shadows form similar triangles, height₁/shadow₁ = height₂/shadow₂.
• Map and scale problems also use similarity: if a 1:50,000 map shows a lake with perimeter 8 cm, the actual perimeter is 8×50,000 cm = 4 km.
• In ladder problems or pyramid problems, always verify which angle is common (usually the angle with the ground or the angle at the apex).

Pythagoras Theorem in Similar Triangles and Right-Angle Configurations

• In right ΔABC with ∠B = 90° and BD ⊥ AC, ΔADB ~ ΔBDC ~ ΔABC by AA (each has a right angle and shares an acute angle).
• From the similarity, BD² = AD×DC (altitude is geometric mean) and AB² = AD×AC, BC² = DC×AC.
• These results underpin the proof of the Pythagoras theorem given in NCERT, making similarity central to Chapter 6 and Chapter 7 both.

Assertion-Reason MCQs in Triangles

• Common traps: R is a correct theorem but applies to a different scenario than A describes, making the answer (B).
• If A is a specific case (e.g. 'ΔABC with sides 3, 4, 5 is right-angled') and R is a general theorem (Pythagoras), R explains A if the numbers satisfy the theorem.
• Practice 10–15 A-R questions before the exam to build the habit of separating truth-value from explanatory linkage.

Common Mistakes and How to Avoid Them

• Inverting a ratio: if you are given AD/DB = 2/3, then DB/AD = 3/2; keep track of which term is in the numerator when setting up proportions.
• Confusing similarity with congruence: similar triangles need not have equal sides, only proportional ones; marking '≅' when you mean '~' is an instant wrong answer.
• Forgetting to square when moving from side ratio to area ratio: if side ratio is 2:5, area ratio is 4:25, not 2:5.
• Skipping the diagram sketch in word problems: a 30-second sketch clarifies which triangles are similar and prevents misidentifying corresponding parts.

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Five More Practice MCQs — Mixed Difficulty

Exam Strategy — How to Attempt MCQs in the CBSE Paper

• Read the question stem completely before looking at options; sometimes the options clarify what the question is really asking.
• In geometry MCQs, if a diagram is provided, mark given information (parallel lines, equal sides) directly on the figure to avoid re-reading.
• For numerical MCQs, do a quick order-of-magnitude check: if the question asks for an area and your answer is negative or absurdly large, you have made an arithmetic error.
• In assertion-reason questions, cover the options first, decide independently whether A is true and whether R is true, then check if R explains A—only then look at the choices.
• If two options are very close numerically (e.g. 8.4 and 8.5), recheck your arithmetic or see if a value was approximated in the question (like π = 3.14 vs 22/7).
• Use the 15-minute rule: allocate roughly 15 minutes to Section A, ensuring you have 75 minutes for the higher-value Sections B, C, D where partial marks exist.