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 Rate this question :

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