Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively.Show that these altitudes are equal​

Answer 1

GIVEN :-

• ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively.

TO SHOW :-

• The attitudes are equal (BE = CF).

SOLUTION :-

✮ In ∆ AEB and AFC,

➳ ∠AEB = AFC. [ Perpendiculars ]

➳ ∠A = ∠A. [ Common angle ]

➳ AB = AC. [ Equal sides of isosceles ∆ ]

Hence ∆ AEB ⩭ ∆ AFC,

➠ BE = CF. [ corresponding part of congruent ∆ ]

Hence proved.

Answer 2

GIVEN :-

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively.

TO SHOW :-

The attitudes are equal (BE = CF).

SOLUTION :-

✮ In ∆ AEB and AFC,

➳ ∠AEB = AFC. [ Perpendiculars ]

➳ ∠A = ∠A. [ Common angle ]

➳ AB = AC. [ Equal sides of isosceles ∆ ]

Hence ∆ AEB ⩭ ∆ AFC,

➠ BE = CF. [ corresponding part of congruent ∆ ]

Hence proved.