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.Assertion (A): The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Reason (R): If two triangles are similar, their corresponding sides are proportional.
- A.Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- B.Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- C.Assertion (A) is true but reason (R) is false.
- D.Assertion (A) is false but reason (R) is true.
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2.In the given figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, which labeled part or property directly confirms that triangle ABC is isosceles?
- A.AX = AY because triangle AXY is isosceles
- B.BX = CY due to the given ratio and AX = AY
- C.∠B = ∠C as they are base angles of triangle ABC
- D.XY is parallel to BC, making the triangles similar
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3.In the given figure, $PQR$ is a triangle right angled at $Q$ and $XY\parallel QR$. If $PQ = 6$ cm, $PY = 4$ cm and $PX:XQ = 1:2$. The length of $PR$ will be
- a.$12 \mathrm{cm}$
- b.$2\sqrt{3} \mathrm{cm}$
- c.$6\sqrt{3} \mathrm{cm}$
- d.$18 \mathrm{cm}$
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4.In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Which of the following statements correctly proves that ΔBPC is similar to ΔABC and determines the length of BP?
- A.ΔBPC ~ ΔABC by SAS similarity because AB/BC = BC/CP = 2 and ∠ABC = ∠BPC; BP = 4 cm
- B.ΔBPC ~ ΔABC by AA similarity because ∠BPC = ∠ABC and ∠BCP = ∠BAC; BP = 6 cm
- C.ΔBPC ~ ΔABC by SSS similarity because all sides are proportional; BP = 2 cm
- D.ΔBPC ~ ΔABC by SAS similarity because AB/BP = BC/CP and ∠ABC = ∠BPC; BP = 8 cm
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5.In the given figure, `
` BC is parallel to DE. Area of triangle ABC = 25 cm², Area of trapezium BCED = 24 cm² and DE = 14 cm. Which labelled segment corresponds to the side BC whose length is 5 cm?- A.The shorter base of trapezium BCED, labelled BC in the figure.
- B.The longer base of trapezium BCED, labelled DE in the figure.
- C.The non-parallel side BD of trapezium BCED.
- D.The side AB of triangle ABC, adjacent to BC.
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