Similarity
ICSE · Class 10 · Mathematics
Practice quiz for Similarity — ICSE Class 10 Mathematics. MCQs and questions with answers to test your preparation.
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If triangle ABC is similar to triangle DEF with sides AB = 6 cm, BC = 8 cm, and DE = 9 cm, find the length of EF.
In triangle ABC, if DE is parallel to BC and AD = 3 cm, DB = 2 cm, AE = 4.5 cm, find EC.
Two similar triangles have areas 36 cm² and 81 cm². If the perimeter of the smaller triangle is 18 cm, find the perimeter of the larger triangle.
In triangle PQR, angle P = 60° and angle Q = 50°. In triangle XYZ, angle X = 60° and angle Y = 70°. Are these triangles similar?
Sample Questions
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.
If the scale factor between two similar triangles is 2:3, find the ratio of their areas.
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4:9
When the scale factor (ratio of corresponding sides) is 2:3, the ratio of areas = (2)²:(3)² = 4:9. Areas of similar figures are proportional to the square of their corresponding linear dimensions.
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).
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