Question

AA criteria theorem​

Answer 1

Answer:

Step-by-step explanation:

The AA criterion for triangle similarity states that if the three angles of one triangle are respectively equal to the three angles of the other, then the two triangles will be similar. In short, equi-angular triangles are similar.

Answer 2

Step-by-step explanation:

Question:-

If two angles of one triangle are respectively equal to two angles of another triangle. Then the Two triangles are similar.

AnswEr:-

Given :- Two triangles ∆ABC and ∆DEF

Such that, ∠B = ∠E & ∠C = ∠F

To prove:-

∆ABC ~ ∆DEF

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To Proof :-

In ∆ABC

∠A + ∠B + ∠C = 180° [ By Angle Sum Property]____eq(1)

Similarly,

In ∆ DEF

∠D + ∠E + ∠F = 180° [By Angle Sum Property] ____eq(2)

From eqn (1) & (2)

↪ ∠A + ∠B + ∠C = ∠D + ∠E + ∠F

↪ ∠A + ∠E + ∠F = ∠D + ∠E + ∠F ( as ∠B = ∠E & ∠C = ∠F)

↪ ∠A = ∠D _____eq (3)

Thus, In ∆ ABC & ∆DEF

↪ ∠A = ∠D [From (3)]

↪∠B = ∠ E [Given]

↪∠C = ∠F [Given]

∴ ∆ ABC ~ ∆DEF [AAA similarity Criteria]

Hence Proved!

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