List of top Mathematics Questions on Criteria for Similarity of Triangles

In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

In the given figure, $AB \parallel EF$. If $AB = 24\text{ cm}$, $EF = 36\text{ cm}$ and $DA = 7\text{ cm}$, then $AE$ equals

Devansh proved that $\Delta ABC \sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C = \angle R$, then which of the following was proved true?

Devansh proved that $\Delta ABC \sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C = \angle R$, then which of the following was proved true?

Devansh proved that $\Delta ABC \sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C = \angle R$, then which of the following was proved true?

In the given figure, DEFG is a square. \(\Delta ABC\) is right angle triangle with \(\angle A = 90^\circ\). Prove that AG \(\times\) DG = AF \(\times\) DB.

D is a point on the side BC of \(\Delta ABC\) such that \(\angle CAB = \angle CDA\). Show that \(CA^2 = CB \times CD\).

In \(\Delta DEF\), \(AB \parallel EF\). The value of \(x\) is :

In $\Delta DEF$, AB $\parallel$ EF. The value of x is :

In the given figure \(\Delta ABC\) is shown, in which \(DE \parallel BC\). If \(AD = 5\text{ cm}\), \(DB = 2\cdot5\text{ cm}\) and \(DE = 8\text{ cm}\), then the length of \(BC\) is :

Shown below are three triangles. The measures of two adjacent sides and included angle are given for each triangle :

Which of these triangles are similar?

In \(\Delta\)ABC, P is a point on AB and Q is a point on AC such that PQ \(\parallel\) BC. If AP : PB = 3 : 2, then PQ : BC is equal to :

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