List of top Mathematics Questions on Criteria for Similarity of Triangles

In the given figure, two triangles ABC and PQR are shown such that \(\angle A = \angle P\) and \(\angle C = \angle R\). If \(AD \perp BC\) and \(PS \perp QR\), then prove that (i) \(\Delta ADB \sim \Delta PSQ\) (ii) \(AD \times QS = BD \times PS\).

In the given figure, \(DE \parallel BC\). If \(AD : AB = 1 : 3\) and \(AE = 2.5\text{ cm}\), then \(AC\) equals

In the given figure, \(\Delta ODC \sim \Delta OBA\). If \(\angle BOC = 110^\circ\), \(\angle ODC = 45^\circ\) and \(AB = 2 CD\), then find (i) \(m\angle OAB\) (ii) \(OB : OD\).

In the given figure, AB $\parallel$ DC. If OB = 3OD and CD = 1.8 cm, then find the length AB.

In the given figure, DE $\parallel$ BC. If AD : AB = 1 : 3 and AE = 2.5 cm, then AC equals