Q. 44.4( 295 Votes )
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32) Show that:
(i) Δ ABE ≅Δ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle
Answer :
It is given in the question that:
BE = CF
(i)
To Prove: 
Proof:
In 
∠A = ∠A (Common)
∠AEB = ∠AFC (Right angles)
BE = CF (Given)
Congruent Triangles - Two angles and an opposite side (AAS) Definition: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.Therefore,
By AAS congruence rule,
(ii) Thus,
AB = AC (By c.p.c.t)
Therefore,
ABC is an isosceles triangle
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