Question

ABC is a triangle in which altitudes BE and CF to
sides AC and AB are equal (see Fig. 7.32). Show
that
(1) A ABE=AACF
() AB = AC, i.e., ABC is an isosceles triangle.​

Answer 1

Answer:

down below

Step-by-step explanation:

in ABE and ACF,

angle E=angleF

angle A is common

be=cf

ABE=ACF

AB=AC (cpct)

Answer 2

Answer:

Given - BE = CF - ( 1 )

BE and CF are altitudes

So, angle AEB =90 degree and angle AFC = 90 degree - ( 2 )

To prove - triangle ABE is congruent to triangle ACF and AB = AC.

Proof - In triangle ABE and ACF

angle AEB = angle AC ( From 2 )

angle A = angle A ( common angle)

BE = CF ( From 1 )

therefore, triangle ABE is congruent to triangle ACF ( AAS rule )

= AB = AC ( CPCT )

Hence Proved