Preparing for the CBSE Class 10 Maths Board Exam? Here are the most important Similarity Theorem Questions (Triangles Chapter) compiled in a clean, easy-to-read list. These textbook-style questions help strengthen concepts of AAA, SSS, SAS similarity, mid-point theorem, and real-life applications.
Important Similarity Questions (One-line format)
1. In Fig. 7.143, ∠A = ∠CED, prove that Δ CAB ~ Δ CED and find the value of x.
2. The perimeters of two similar triangles are 25 cm and 15 cm. If one side of the first triangle is 9 cm, find the corresponding side of the other.
3. In Δ ABC and Δ DEF, AB = 5 cm, BC = 4 cm, CA = 4.2 cm; DE = 10 cm, EF = 8 cm, FD = 8.4 cm. If AL ⟂ BC and DM ⟂ EF, find AL : DM.
4. In Δ ABC, D ∈ AB and E ∈ AC such that AD = 8 cm, DB = 12 cm, AE = 6 cm, CE = 9 cm; prove that BC = 5/2 DE.
5. D is the mid-point of BC of Δ ABC. AD is bisected at E and BE meets AC at X. Prove that BE : EX = 3 : 1.
6. ABCD is a parallelogram. APQ meets BC at P and DC (produced) at Q. Prove that BP × DQ = AB × BC.
7. In Δ ABC, AL ⟂ BC and CM ⟂ AB intersect at O. Prove that (i) ∠OMA ~ ∠OLC (ii) OA/OC = OM/OL.
8. In quadrilateral ABCD, AD = BC. P, Q, R, S are mid-points of AB, AC, CD, BD. Prove that PQRS is a rhombus.
9. In an isosceles Δ ABC, AB is produced both ways to P and Q such that AP × BQ = AC². Prove that Δ APC ~ Δ BCQ.
10. A 90 cm tall girl walks away from a lamp-post at 1.2 m/sec. The lamp height is 3.6 m. Find the length of her shadow after 4 seconds.
11. A vertical stick of 6 m casts a 4 m shadow. A tower at the same time casts a 28 m shadow. Find the tower’s height.
12. In Fig. 7.144, Δ ABC is right-angled at C and DE ⟂ AB. Prove that Δ ABC ~ Δ ADE and find AE and DE.
13. In trapezium ABCD, AB ∥ DC and diagonals AC and BD intersect at O. Show that OA/OC = OB/OD.
14. Δ ABC and Δ AMP are right-angled at B and M respectively; ∠MAP = ∠BAC. Prove that (i) Δ ABC ~ Δ AMP (ii) CA/PA = BC/MP.
15. A 10 cm vertical stick casts an 8 cm shadow. A tower at the same time casts a 30 m shadow. Find the tower’s height.