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

Question

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32) Show that: (i) &#x394; ABE &#x2245; &#x394; ACF (ii) AB = AC, i.e., ABC is an isosceles triangle

Philoid · Accepted Answer

It is given in the question that:

BE = CF

(i) In

∠A = ∠A (Common)

∠AEB = ∠AFC (Right angles)

BE = CF (Given)

Therefore,

By AAS axiom,

(ii) Thus,

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

Therefore,

ABC is an isosceles triangle

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

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