Q. 113.7( 6 Votes )

# ΔABC is an equila

Answer : Δ ABC is an equilateral triangle.

Also, BC = AB = AC = 2a

The AD, CE, and BF are the altitude at BC, AB and AC respectively. Therefore, D, E, and F are the midpoint of BC, AB and AC respectively.

Now, ΔADB and ΔADC are right-angled triangles.

Applying Pythagoras theorem,

AB2 = BD2 + AD2

(2a) 2 = a2 + AD2

AD2 = 3a2

AD = a√3 units

Similarly ΔACE and ΔBEC are right-angled triangles.

Applying Pythagoras theorem,

CE = a√3 units

And ΔABF and ΔBFC are right-angled triangles.

Applying Pythagoras theorem,

BF = a√3 units

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