Question

prove that in a rhombus with angle of 60°, the shorter diagonal divides the rhombus into two equilateral triangles

Answer 1

Answer :-

In ∆ADC, we have,

→ ∠ADC = 60° (given)

→ AD = DC (sides of rhombus are equal in length.)

so,

→ ∠DAC = ∠DCA (Angle opposite to equal sides are equal in measure.)

then,

→ ∠ADC + ∠DAC + ∠DCA = 180° (Angle sum property.)

→ 60° + 2∠DCA = 180°

→ 2∠DCA = 180° - 60°

→ ∠DCA = 120°/2 = 60°

therefore,

→ ∠ADC = ∠DAC = ∠DCA = 60° .

since all angles are equal to 60°. Hence, ∆ADC is a equaliteral triangle .

now, in Rhombus ,

→ ∠ABC = ∠ADC = 60° (Opposite angles of a rhombus are equal.)

then, similarly, we can conclude that, ∆ABC is also a equaliteral triangle .

Hence, we can conclude that, the shorter diagonal divides the rhombus into two equilateral triangles .

Learn more :-

ABCD is a rhombus with A = 60° , BC = (3x+5)cm , CD =(6x-10)cm and AC =(3y-1)cm. Find

x and y.

please urgent please

n...

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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