Question

ABC is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal. Then:

• A. $△ABE\cong △ACF$
• B. $AB=AC$ i.e, ABC is an isosceles triangle.
• C. $\angle ABC=\angle ACB$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $△ABE\cong △ACF$
B $AB=AC$ i.e, ABC is an isosceles triangle.
C $\angle ABC=\angle ACB$

In $△ABE$ and $△ACF$,

we have $\angle A=\angle A$ (Common)

$\angle AEB=\angle AFC$ (Each=${90}^0$)

$BE=CF$ (Given)

$\therefore △ABE\cong △ACF$ (By SAS congruence rule)

$\Rightarrow AB=AC$ (By CPCT)

$\therefore \Delta ABC$ is an isosceles triangle.

$\Rightarrow \angle ABC=\angle ACB$