In the given pairs of triangles, find which pair of triangles are similar. State the similarity criterior and write the similarity relation in symbolic from.
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In $\triangle\text{ABC}$ and $\triangle\text{EFD}$
$\angle\text{A}=\angle\text{D}=70^\circ$
SAS: Similarity condition is not satisfied as $\angle\text{A}$ and $\angle\text{D}$ are not included angles.
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D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}.$ In the following cases, determine whether DE || BC or not. AD = 7.2cm, AE = 6.4cm, AB = 12cm and AC = 10cm.
Two triangles DEF and GHK are such that $\angle\text{D}=48^\circ$ and $\angle\text{H}=57^\circ.$ If $\triangle\text{DEF}\sim\triangle\text{GHK}$ then find the measure of $\angle\text{F}.$
In the given figure, $\angle\text{CAB}=90^\circ$ and $\text{AD}\perp\text{BC}.$ Show that $\triangle\text{BDA}\sim\triangle\text{BAC}.$ If AC = 75cm, AB = 1m, and BC = 1,25m find AD.
The corresponding sides of two similar triangles are in the ratio $2 : 3$. If the area of the smaller triangle is $48\ cm^2$, find the area of the larger triangle.
The corresponding sides of two similar triangles are in the ratio $2 : 3.$ If the area of the smaller triangle is $48\ cm^2,$ find the area of the larger triangle.
In a trapezium ABCD, it is given that AB || CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that $\text{ar}(\triangle\text{AOB})=84\text{cm}^2.$ Find $\text{ar}(\triangle\text{COD}).$
In the given figure, O is a point inside a $\triangle\text{PQR}$ such that $\angle\text{PQR}=90^\circ,\text{OP}=6\text{cm}$ and $\text{OR}=8\text{cm}.$ If $\text{PQ}=24\text{cm}$ and $\text{QR}=26\text{cm},$ prove that $\triangle\text{PQR}$ is right-angled.