Question

In fig. 2, MN || BC and AM: MB = 1:2, then
ar(AMN)
ar( ABC) =

Fig.-2​

Answer 1

1/9 is the ar(AMN) /ar( ABC).

Step-by-step explanation:

Given,

AM : MB = 1:2

so, MB/AM = 2/1

By adding 1 to both sides,

⇒ MB/AM + 1 = 2/1 + 1

⇒ MB + AM/AM = (2 + 1)/1

⇒ AB/AM = 3/1

In the ΔAMN and ΔABC,

∠AMN = ∠ABC  (∵ corresponding angles in MN ║ BC)

∠ANM = ∠ACB   (∵ corresponding angles in MN ║ BC)

Using AA criteria,

ΔAMN ≅ ΔABC

If the triangles are similar, the ratio of the areas is equal to the ratio of the corresponding sides' square;

∵ ar(ΔAMN)/ar(ΔABC) = (AM/AB)^2

= (1/3)^2

= 1/9

Thus, ar(AMN) /ar( ABC) = 1/9

Learn more: Triangle

brainly.in/question/13401128