State the two properties which are necessary for given two triangles to be similar.
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Two triangles are said to be similar to each other if:
Their corresponding angles are equal.
Their corresponding sides are proportional.
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A vertical pole of lenght 7.5m casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.
$\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $\text{ar}(\triangle\text{ABC})=64\text{cm}^2$ and $\text{ar}(\triangle\text{DEF})=169\text{cm}^2.$ If BC = 4cm, find EF.
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.
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.