one of the diagonal of a rhombus is equal to one of its sides. find the angle of the rhombus
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ABCD is a rhombus.
⇒AC=BC ........(1)(given)
BC=AB .....(2)(side of rhombus)
From eqns(1) and (2)
AC=BC=AB
⇒△ABC is equilateral triangle.
So, ∠ABC=60
∘
∠BCA=60
∘
..........(3)
∠CAB=60
∘
..........(4)
Similarly, in △ADC,AD=DC(sides of a rhombus)
AD=BC
But BC=AC
∴AD=AC
∴AD=DC=AC
∴DAC is an equilateral triangle.
⇒∠CAD=60
∘
......(5)
⇒∠ADC=60
∘
⇒∠DCA=60
∘
.......(6)
From eqns(3) and (6) we get
∠BCA+∠DCA=60
∘
+60
∘
=120
∘
∴∠C=120
∘
From eqns(4) and (5),
∠CAB+∠CAD=60
∘
+60
∘
=120
∘
∴∠A=120
∘
Hence the four angles of the Rhombus are 120
∘
,60
∘
,120
∘
,60
∘
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