List of top Mathematics Questions on Similarity of Triangles

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 $AD = BC$.

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: