Similarity
ICSE · Class 10 · Mathematics
Most important questions from Similarity for ICSE Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Which of the following are conditions for triangle similarity? (Select all correct answers)
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AA (Angle-Angle), SSS (Side-Side-Side proportional), SAS (Side-Angle-Side proportional)
The three conditions for triangle similarity are: AA (two angles equal), SSS (all three sides proportional), and SAS (two sides proportional with included angle equal). ASA and RHS are congruence conditions, not similarity.
In a triangle ABC, D and E are points on AB and AC such that DE || BC. If AD = 4 cm, AB = 10 cm, and AC = 15 cm, find AE.
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6 cm
By Basic Proportionality Theorem, AD/AB = AE/AC → 4/10 = AE/15 → AE = (4 × 15)/10 = 60/10 = 6 cm
Which of the following statements about similar triangles are true? (Select all correct)
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Corresponding angles are equal, Corresponding sides are proportional, All congruent triangles are similar
Similar triangles have equal corresponding angles and proportional corresponding sides. All congruent triangles are similar (same shape and size), but not all similar triangles are congruent (they may have different sizes).
Two triangles have sides in the ratio 3:4. If the area of the smaller triangle is 27 cm², find the area of the larger triangle.
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48 cm²
Side ratio = 3:4, so area ratio = 3²:4² = 9:16. If smaller area = 27 cm², then larger area = (16/9) × 27 = 16 × 3 = 48 cm²
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