Question

In each of the following figures, you find who triangles. Indicate whether the triangles are similar. Give reasons in support of your answer.

(i)

(ii)


(iii)


(iv)


(v)

Answer 1

(i) In two triangles, we observe that

In similar triangle corresponding sides are proportional to each other.

Therefore, by SSS-criterion of similarity,

two triangles are similar

(ii)

PQ || BC (Corresponding angles formed are equal)

In ΔAPQ and ΔABC,

$\angle APQ=\angle B\left(\mathrm{Corresponding}\mathrm{angles}\right)$

$\angle PAQ=\angle BAC\left(\mathrm{Common}\right)$

So, $∆\mathrm{APQ}~∆\mathrm{ABC}$ (AA Similarity)

two triangles are similar

(iii) In two triangle, we observe that

In ΔABC and ΔCDE

$\frac{CD}{CE}=\frac{CB}{CA}$

$\angle ACB=\angle DCE$ (Vertically opposite angles)

ΔABC $~$ ΔCDE (SAS Similarity)

two triangles are similar

(iv) In two triangle, we observe that

In two triangles corresponding sides are not proportional to each other.

two triangles are not similar.

(v) In two triangle, we observe that

In two triangles corresponding sides are not proportional to each other.

two triangles are not similar.