Solve this: 10 â ‹In the adjoining figure, AD, BE and CF are altitudes of △ABC - Maths - Triangles

Question

Solve this:

10 â€‹In the adjoining
figure, AD, BE and CF are altitudes of △ ABC If AD = BE = CF,
prove that ABC is an equilateral triangle

Chat_4 · Accepted Answer

Dear Meezan

As Per Your Given Image AD, BE and CF are altitudes of
â–³ABC If AD = BE = CF,
We have
â€‹â€‹â€‹â€‹â€‹
triangle ABE and triangle ACF
BE=CF (Given )
∠A=∠A (Common Angle )
∠AEB=∠AFC=90°
By congruent rule ABE ≅ ACF
AB=AC
Similarly
BCF ≅ ABD
AB=BC
AC=BC
AB=AC
AB = BC = AC
That means ABC is equilateral triangle

Regards

Solve this: 10. ​In the adjoining figure, AD, BE and CF are altitudes of △ ABC. If AD = BE = CF, prove that ABC is an equilateral triangle.

Solve this:

10. In the adjoining figure, AD, BE and CF are altitudes of $△$ ABC. If AD = BE = CF, prove that ABC is an equilateral triangle.