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

( Common angle)

(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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