Tag: similarity of triangles

Triangles are similar if they have the same shape, but not necessarily the same size.   It is same as keeping its basic shape but either "zooming in" or out making the triangle bigger or smaller .

For triangles to be congruent if one triangle slides over the other , rotate them, and flip them over in various ways so they will exactly fit over each other.

So, if the triangles are similar, i.e. they are "zoomed-in" or "zoomed-out" versions of each other, and if they have equal area, then they are congruent, and hence have equal corresponding sides.

Since, ratio of area of two similar traingles = ratio of square of corresponding sides

$\displaystyle \because \Delta ABC\sim \Delta DEF$
$\displaystyle \therefore \dfrac{ar\Delta ABC}{ar\Delta DEF}=\dfrac{\left ( 4 \right )^{2}}{\left ( 9 \right )^{2}}=\dfrac{16}{81}=16:81.$

$\sim$ is used to represent similarity.

When the ratios of the lengths of their corresponding sides are equal, then the two figures are then those figure are similar by $SSS$ similarity.

Two similar triangles can be represented as $ABC∼PQR.$

Congruent figures are of same shape and size. So they are similar but similar figures are not congruent as they might not be of the same size.
Therefore, C is the correct answer.

If the ratio of the tree is 3 : 2 = 24 m : 16 m 
The ratio of the pole is  same so 48m : 32m
Therefore, B is the correct answer.

They are said to be similar as the shape is same but size differs.
Therefore, B  is the correct answer.

All Equilateral  triangles , corresponding angles are equal .So, they are similar.
Therefore, C is the correct answer.