ABC is triangle in which altitudes BE and CF to sides AC and AB are equal. How many of the following are true:
(a) ΔABE≅ΔACF
(b) AB=AC, i.e., is an isosceles triangle.
GivenBE=CF−(1)
BE&CFarealtitudes
so∠AEB=90∘and∠AFC=90∘−(2)
toshow:ΔABE≅ΔACF&
AB=AC
InΔABEandΔACF
∠AEB=∠AFC
∠A=∠A[from(2)]
BE=CFfrom(1)
ΔABE≅ΔACF(AAScongruencerule)
AB=AC(CDCT)