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