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ABCD is a rhombus. Diagonal AC divides it into equilateral triangles. FADO = 60 find ZABC and _DCB. |
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Answer» Let ABCD is a rhombus. AC and BD are diagonals such that, AC is EQUAL to all sides of rhombus.⇒ AB = BC = CD = DA = Diagonal AC.⇒ In △ABC,⇒ AB = BC = AC [Given]∴ △ABC is an EQUILATERAL triangle.⇒ So, ∠CAB = ∠ABC = ∠ACB = 60 ∘ [Angles of equilateral triangle] --- ( 1 )⇒ Similarly, in △ADC we get,⇒ ∠CAD = ∠ADC =∠ACD = 60 ∘ ----- ( 2 )⇒ ∠BAD = ∠BAC + ∠CAD = 60 ∘ + 60 ∘ = 120 ∘ -- ( 3 )⇒ ∠BCD = ∠BCA + ∠ACD = 60 ∘ + 60 ∘ = 120 ∘ ---- ( 4 )So, from ( 1 ), ( 2 ), ( 3 ) and ( 4 ) we get,The angles of a rhombus ABCD are 120 ∘ ,60 ∘ ,120 ∘ ,60 ∘ . |
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