Question

please help me please yaar please ​

Answer 1

Given :-

• AB = AC
• BE & CF are bisector of ∠B and ∠C respectively

To prove :-

• BE = CF

Solution :-

We use the concept of congruency to solve this problem.

Since BE and CF are bisectors of angle B and C, this implies that:-

➝ ∠ABE = ∠EBC

➝ ∠ACF = ∠BCF

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Also AB = AC implies that :-

➝ ∠ B = ∠ C [ angle opposite to equal sides ]

➝ ∠ABE = ∠EBC = ∠ACF = ∠BCF

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Now consider ∆ ABE and ∆ ACF :-

➝ ∠ A = ∠A [ Common in both triangles ]

➝ AB = AC [ Given ]

➝ ∠ ABE = ∠ ACF [ Proved above ]

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Hence ∆ ABE is congruent to ∆ ACF

➝ BE = CF [ By C.P.C.T. ]

Answer 2

can be proved by SAS criteria

as in triangle FBC and triangle EBC :-

FB=EC ( given )

Angle FBC =Angle ECB ( opposite angles of isoselous triangles are equal )

BC =CB ( common side )

thus , ️FBC is congurent to ️EBC by SAS .

hence , BE= CF