Maths-
General
Easy

Question

ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
(i) ΔABE ⩭ ΔACF
(ii)  AB = AC

Hint:

Find the congruence rule used and then find whether the sides are equal.

The correct answer is: AB = AC




    (i) In ΔABE and ΔACF, we have
    straight angle B A E equals straight angle C A F ( Common angle)
    straight angle A E B equals straight angle A F C (Since BE ⟂ AC and CF ⟂  AB)
    BE = CF (given)
    Hence, by AAS criterion ΔABE  ⩭ ΔACF
    (ii) Since ΔABE  ⩭  ΔACF, we have
    AB = AC (Corresponding part of congruent triangles)

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