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.

Sample questions

1. 1.If $\Delta ABC \sim \Delta APQ$ and $\operatorname{ar}(\Delta APQ) = 4 \operatorname{ar}(\Delta ABC)$, then the ratio of $BC$ to $PQ$ is
   • a.$2:1$
   • b.$1:2$
   • c.$1:4$
   • d.$4:1$
2. 2.If ratio of corresponding sides of two similar triangles is 5:6, then ratio of their areas will be: Options:
   • A.25:36
   • B.5:6
   • C.36:25
   • D.6:5
3. 3.In ΔABC, ∠ACB = 90° and CD ⊥ AB. Which of the following correctly proves that BC²/AC² = BD/AD?
   • A.ΔACD ∼ ΔBCD by AA similarity, so AC/BC = AD/CD = CD/BD, leading to BC²/AC² = BD/AD.
   • B.ΔACD ∼ ΔABC by AA similarity, so AC/BC = AD/AB = CD/BC, leading to BC²/AC² = BD/AD.
   • C.ΔACD and ΔBCD are congruent, so AC = BC and AD = BD, leading to BC²/AC² = BD/AD.
   • D.ΔACD ∼ ΔCBD by SAS similarity, so AC/BC = AD/BD, directly giving BC²/AC² = BD/AD.
4. 4.Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting diagonal AC in L and AD produced in E. Which of the following correctly relates EL and BL?
   • A.EL = BL
   • B.EL = 2BL
   • C.EL = 3BL
   • D.BL = 2EL
5. 5.In the given figure, $P$ and $Q$ are points on the sides $AB$ and $AC$ respectively of a triangle $ABC$. $PQ$ is parallel to $BC$ and divides the triangle $ABC$ into 2 parts, equal in area. The ratio of $PA:AB =$
   • a.$1:1$
   • b.$(\sqrt{2} - 1):\sqrt{2}$
   • c.$1: \sqrt{2}$
   • d.$(\sqrt{2} - 1):1$