Mathematics
Assertion (A) : One of the diagonals of rhombus is equals to one of its side. The angles of a rhombus are 60°, 120°, 60°, 120°.
Reason (R) : All the sides of a rhombus are equal.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Quadrilaterals
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Answer
By property,
All the sides of a rhombus are equal.
So, reason (R) is true.
ABCD is the rhombus and AC is the diagonal such that AC = AB.
In triangle ABC,
⇒ AB = BC (Sides of rhombus are equal)
⇒ AB = AC (Given)
⇒ AB = AC = BC
So, triangle ABC is an equilateral triangle.
∴ ∠B = 60°, ∠BAC = 60° and ∠BCA = 60°.
In triangle ADC,
⇒ AD = CD (Sides of rhombus are equal)
⇒ AD = AC (Since, AB = AC and AB = AD)
⇒ AD = CD = AC
So, triangle ADC is an equilateral triangle.
∴ ∠D = 60°, ∠DAC = 60° and ∠DCA = 60°
⇒ ∠A = ∠BAC + ∠DAC = 60° + 60° = 120°.
⇒ ∠C = ∠BCA + ∠DCA = 60° + 60° = 120°.
Hence, the angles of a rhombus are 60°, 120°, 60°, 120°.
So, assertion (A) is true.
∴ Both A and R are correct, and R is not the correct explanation for A.
Hence, option 2 is the correct option.
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