Question

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that. 1) ABE is congruent to ACF. 2) AB=AC i.e. ABC is an isosceles triangle.

Answer 1

⭐Here is your answer⭐

Given That,

ABC is a ∆ in which BE and CF are altitudes.

So that, <AEB= <AFC= 90°

Then To prove that,

∆ABE Congruent to ∆ACF and AB=AC,

Proof:- In ∆ABE and ∆ACF,

<AEB= <AFC= 90°

<A = <A (common)

BE= CF (Given)

∆ABE Congruent to ∆ACF (A.A.S rule)

Hence,

AB=AC (C.P.C.T or Corresponding Parts of Congruent ∆).

Proved

Be Brainly

Answer 2

Answer:

( I) in triangle ABE and triangle ACD we have BE = CF ( given )

angle BAE = Angle CAE ( common )

angle BEA = angle CFA ( each 90 degree)

so , triangle ABE congruent to triangle ACD ( AAS ) proved

(ii) also AB equals to AC ( CPCT)

so that

ABC is an isosceles triangle proved