ICSE Class 10 Similarity of Triangles — Mock Test (2027)
Free online mock test for Similarity of Triangles (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Similarity of Triangles chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.In the given figure, AB and DE are perpendiculars to BC. If AB = 9 cm, DE = 3 cm, and AC = 24 cm, calculate AD.
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2.In the given diagram, $\triangle ABC \sim \triangle PQR$ and $\frac{AD}{PS} = \frac{3}{8}$. The value of $AB:PQ$ is:
- a.$8:3$
- b.$3:5$
- c.$3:8$
- d.$5:8$
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3.D is a point on the side BC of triangle ABC such that angle ADC is equal to angle BAC. Which of the following correctly proves that CA² = CB × CD?
- A.Since ∠ADC = ∠BAC and ∠ACD = ∠BCA, ΔADC ~ ΔBAC by AA similarity, so CA/CB = CD/CA ⇒ CA² = CB × CD.
- B.Using the Pythagorean theorem on ΔADC and ΔBAC, we derive CA² = CB × CD.
- C.Since ∠ADC = ∠BAC, ΔADC ≅ ΔBAC by AA congruence, so CA = CB and CD = CA ⇒ CA² = CB × CD.
- D.By the power of point D, CA² = CD × DB, which simplifies to CA² = CB × CD.
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4.$\Delta ABC$ is an equilateral triangle with each side of length $2p$. If $AD \perp BC$ then the value of $AD$ is
- a.$\sqrt{3}$
- b.$\sqrt{3} p$
- c.$2p$
- d.$4p$
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5.In the given figure, $DE \parallel BC$. What is the value of $x$?
- A.1
- B.2
- C.3
- D.4
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