ABCD is a rhombus in which aktitude from D to side AB bisects AB find the angle of rhombus.
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In a ΔAED and ΔBED,
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
DE = DE ( common line)
∠AED = ∠BED ( right angle)
AE = EB ( DE is an altitude)
∴ ΔAED ≅ ΔBED ( SAS property)
∴ AD = BD ( by C.P.C.T)
But AD = AB ( sides of rhombus are equal)
⇒ AD = AB = BD
∴ ABD is an equilateral traingle.
∴ ∠A = 60°
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