Question

Which pairs of triangles are similar? Check all that apply.

Answer 1

option (2) and (5) are correct.

ΔABC ≅ ΔJLK

ΔDEF ≅ ΔGHI

Explanation:

Given four right angled triangle with measure of sides.

We have to check for the pairs of triangle to be similar.

Two triangles are said to be similar if their corresponding angles are equal or their corresponding sides are same ratio.

Consider, ΔABC and ΔJLK.

∠C = ∠L = 90° (given)

Also ratio of corresponding sides are same ratio, that is

`(AC)/(LJ)=(14)/(7)=(2)/(1)`

Also,
`(CB)/(KL)=(20)/(10)=(2)/(1)`

Thus, ΔABC ≅ ΔJLK.

Option (5) is correct.

Consider, ΔDEF and ΔGHI.

∠I = ∠F = 90° (given)

Also ratio of corresponding sides are same, that is

`(DF)/(GI)=(8)/(12)=(2)/(3)`

Also,
`(EF)/(HI)=(10)/(15)=(2)/(3)`

Thus, ΔDEF ≅ ΔGHI.

Option (2) is correct.

Thus, option (2) and (5) are correct.