Question

abcd is a rhombus in which the altitude from d to side ab bisects ab find the angles of rhombus​

Answer 1

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Answer 2

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

In a ΔAED and ΔBED

DE =DE (common line)

<AED = < BED ( right angle)

AE = BE ( DE is an altitude)

therefore ΔAED =~(congrunt) ΔBED (SAS property)

therefore AD = BD (by C.P.C.T.)

But AB =AB (sides of rhombus are equal)

=> AB = AB = BD

therefore ABD is an equalateral triangle.

therefore <A = 60°

=> <A = <C = 60° (opposite angle of rhombus is equal)

But sum of adjacent of a rhombus is supplimentary.

<ABC + BCD = 180°

=> <ABC + 60° = 180°

=> <ABC = 180° - 60° = 120°.

therefore <ABC = ADC = 120° (opposite angle of a rhombus are equal)

therefore angles of a rhombus are <A = 60° and <C = 60° , <B <D = 120°.

HOPE THIS HELPS.

THANK YOU.