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,

Hence, Proved.

(ii) Thus,

AB = AC (By c.p.c.t)

Therefore,

ABC is an isosceles triangle

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