# If the altitudes of a triangle ABC are equal,then prove that triangle is equilateral.

Given, AD, BE and CF are the attitudes drawn on sides BC, CA and AB of Δ ABC such that AD = BE = CF

Area of Δ ABC = × BC × AD =  × AB × CF =  × CA × BE (Area of Δ =  × Base × Correspondence attitude)

∴ BC × AD = AB × CF = CA × BE

⇒ BC = AB = CA ( AD = BE = CF)

Hence, ΔABC is an equilateral triangle.

• 60

Prove tht the bisectors of the angles of a linear pair are right angles

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prove tht the measure of each angle of an equalateral triangle is 60

solve this one nt the above one plzzz i got  tht

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 Steps Statement Reason 1 Consider triangles BEC and BFC 2 EC=BF Equal altitudes(given) 3 BEC=BFC = 900 BE and BF are Altitudes 4 BC is common 5 BEC BFC RHS postulate 6 ABC = BCA Corresponding angles 7 Consider the ADB and ADC 8 ADB=ADC = 900 AD is Altitude 9 AD is common 10 ABC = BCA Step 6 11 ADB ADC ASA postulate 12 AB =AC Corresponding sides are equal 13 BC= AC Similarly we can prove BFC BFA 14 AB=AC=BC Step 12,13

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