# Show that each diagonal of a rhombus bisects the angle through which it passes.

(i) In ΔBOC and ΔDOC

BO = DO [In a rhombus diagonals bisect each other]

CO = CO Common

BC = CD [All sides of a rhombus are equal]

ΔBOCΔDOC [SSS Congurency]

BCO =DCO from above [corresponding parts of congruent triangles]

Hence, each diagonal of a rhombus bisect the angle through which it passes.

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RELATED QUESTIONS :

Which of the following statements are true for a rhombus?

(ii) It has two pairs of equal sides.

(iii) It has only two pairs of equal sides.

(iv) Two of its angles are at right angles.

(v) Its diagonals bisect each other at right angles.

(vi) Its diagonals are equal and perpendicular.

(vii) It has all its sides of equal lengths.

(viii) It is a parallelogram.