Question

Which pairs of polygons are similar? Plz help

Answer 1

Option (1) and (3)

Explanation:

Properties for the similarity of two figures,

1). Angles of the figures should be same.

2). Corresponding sides of both the figures should be proportional.

Since all the pairs have same angles, we will use the second property to prove these polygons similar.

Option (1)

If both the polygons are similar,

`(3)/(7.5)=(5)/(12.5)`

`(1)/(2.5)=(1)/(2.5)`

Since, sides are proportional,

Both the polygons are similar.

Option (2)

If the given triangles are similar,

Ratio of the sides of both the triangles will be proportional,

`(18)/(8)= (24)/(15)`

`(19)/(4)=(8)/(5)`

But
`(19)/(4)\\eq (8)/(5)`

Therefore, triangles are not similar.

Option (3)

If both the rectangles are similar,

`(22)/(13.75)=(16)/(10)`

1.6 = 1.6

True.

Therefore, both the rectangles are similar.

Option (4)

If both the triangles are similar,

`(8)/(5)=(7)/(5)`

1.6 = 1.2

But 1.6 ≠ 1.2

Therefore, these triangles are not similar.