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Concurrency of Altitudes of a Triangle

20. AD is an ...

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20. AD is an altitude of an equilateral triangle ABC . On AD as base , another equilateral triangle ADE is drawn . Prove that Ar(ΔABE):Ar(ΔABC)=3:4

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Q. AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed.
Prove that Area (∆ADE) : Area (∆ABC) = 3 : 4.

A D

is an altitude of

c m

△ A B C

A D

base another equilateral triangle

A D E

is construct then

a r (△ A D E) : a r (△ A B C) = 3 : 4

Q. In an equilateral triangle

A B C

A D

is the altitude drawn from

A

B C

3 {A B}^{2} = 4 {A D}^{2}

.

Q. In adjoining figure,

A D, B E

C F

are altitudes of

△ A B C

A D = C F = B E .

A B C

is an equilateral triangle.

Q. AD,BE and CF, the altitudes of triangle ABC are equal. Prove that triangle ABC is an equilateral triangle.

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