Question

best answer will be marked brainliest....​

Answer 1

Answer:

AA Criterion :-

If two angles of a triangle are respectively equal to two angles of another triangle ,then the other two triangles are similar.

Given :-

Two triangles ABC and DEF such that ,

angle B = angle E and angle C = angle F

To prove :-

Triangle ABC ~ Triangle DEF

Proof :-

In triangle ABC ,

Angle A + Angle B + Angle C = 180° ( Angle Sum property) ------- (i)

In triangle DEF ,

Angle D + Angle E + Angle F = 180° (Angle sum property) --------(ii)

From (i) and (ii) ,

<A + <B + <C = <D + <E + <F

<A + <E + <F = <D + <E + <F

<A = <D ------- (iii)

Thus,

In triangle ABC & DEF,

Angle A = Angle D

Angle B = Angle E

Angle C = Angle F

☆Triangle ABC ~ Triangle DEF•(By AA-Similarity)

Hence proved!