Q. 44.0( 22 Votes )

ABCD is a rhombus

Answer :


Given,


ABCD is a rhombus.DE is the altitude on AB then AE = EB.


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 triangle.
A = 60
A = C = 60 (opposite angles of rhombus are equal)
But Sum of adjacent angles of a rhombus is supplementary.
ABC + BCD = 180
ABC + 60 = 180
ABC = 180-60 = 120
ABC = ADC = 120 (opposite angles of rhombus are equal)
Angles of rhombus are A = 60, C = 60, B = 120, D = 120


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