Question

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.​

Answer 1

$\huge\mathbb{SOLUTION:-}$

Given:-

• ABCD is a rhombus. Diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

Explanation:-

ABCD is a rhombus.

AC and BD are its diagonals.

Proof,

AD = CD (Sides of a rhombus)

∠DAC = ∠DCA (Angles opposite of equal sides of a triangle are equal.)

also, AB || CD

⇒ ∠DAC = ∠BCA (Alternate interior angles)

⇒ ∠DCA = ∠BCA

AC bisects ∠C.

Similarly,

We can prove that diagonal AC bisects ∠A.

Following the same method,

• We can prove that the diagonal BD bisects ∠B and ∠D.