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One of the diagonals of a rhombus and its sides are equal. Find the angles of therhombus. |
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Answer» 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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