List of top Mathematics Questions on 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, $PQ \parallel YZ$ such that $XP : PY = 2 : 3$. If $PQ = 5\text{ cm}$, then $YZ$ equals

In the given figure, $PQ \parallel YZ$ such that $XP : PY = 2 : 3$. If $PQ = 5\text{ cm}$, then $YZ$ equals

It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?

It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?

ABCD is a parallelogram such that AF = 7 cm, FB = 3 cm and EF = 4 cm, length FD = equals

It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?

If \(\Delta DEF \sim \Delta PQR\) such that \(3 DE = PQ\) and \(EF = 6\) cm, then the length of QR is :

If $\Delta$ ABC and $\Delta$ DEF are similar such that $2 \text{ AB} = \text{DE}$ and $\text{BC} = 8 \text{ cm}$, then EF is equal to :

It is given that \(\Delta ABC \sim \Delta QRP\) such that \(AB = 9\text{ cm}\), \(BC = 5\text{ cm}\) and \(PR = 2\text{ cm}\). Length of side \(QR\) is :

It is given that $\Delta ABC \sim \Delta QRP$ such that $AB = 9$ cm, $BC = 5$ cm and $PR = 2$ cm. Length of side QR is :

In triangles ABC and PQR, \(\angle A = \angle Q\) and \(\angle B = \angle R\), then AB : AC is equal to :

If $\Delta ABC$ and $\Delta DEF$ are similar such that $2 AB = DE$ and $BC = 8\text{ cm}$, then $EF$ is equal to :

If in two triangles ABC and DEF, \(\frac{AB}{EF} = \frac{BC}{DE} = \frac{CA}{DF}\); then :

If the ratio of corresponding sides of two similar triangles is \(2:7\), then the ratio of the areas of the triangles is _____.

Reduced and enlarged photographs of an object are _____.

\( \triangle ABC \sim \triangle DEF \) and their areas are respectively \(75 \text{ cm}^2\) and \(48 \text{ cm}^2\). If \(EF = 4 \text{ cm}\), then \(BC = \_\_\_\_\_ \text{ cm}\).

In \( \triangle ABC \), \( DE \parallel BC \), \( \frac{AD}{DB} = \frac{2}{3} \) and \( AC = 2.5 \text{ cm} \), then \( AE = \_\_\_\_\_ \text{ cm}\).

In \( \triangle ABC \), \( DE \parallel AB \), \( AD = x + 1 \), \( CD = x + 3 \), \( BE = x + 4 \) and \( CE = x + 7 \), then the value of \( x \) is _____.

Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that \(PS = 9\) cm, \(PQ = 35\) cm, \(BR = x\), \(\angle PRQ = \alpha\) and \(\angle CRB = \theta\). Based on the above information, answer the following questions:

$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.

If $\triangle ABC \sim \triangle DEF$ and $AB = 4$ cm, $DE = 6$ cm, $EF = 9$ cm, and $FD = 12$ cm, find the perimeter of $\triangle ABC$.

In a $\triangle ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $BD = CE$. If $\angle B = \angle C$, then show that $DE \parallel BC$.

If in triangles $ABC$ and $PQR$, $\frac{AB}{QR} = \frac{BC}{PR}$, then they will be similar, when:

$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.