Question

if all the three attitudes of a triangle are equal then prove that it is an equilateral triangle.​

Answer 1

Step-by-step explanation:

Consider triangles BEC and BFC

EC=BF (Equal altitudes: Given)

∠BEC=∠BFC=90 (BE and BF are Altitudes)

BC = BC (common)

△BEC≅△BFC (RHS postulate)

∠ABC=∠BCA (Corresponding angles)

Consider the △ ADB and △ ADC

∠ADB=∠ADC=90 (AD is Altitude)

AD = AD (common)

∠ABC=∠BCA

Thus, △ADB≅△ADC (ASA postulate)

AB =AC (Corresponding sides are equal)

BC= AC (Similarly, we can prove △BFC≅△BFA)

Thus, AB=AC=BC