Question

abcd is a rhombus and its diagonals intersect at o.

i) is ∆aob congruent to ∆boc ? state the congruence condition used.
ii)also state if angle BCO = angle DCO. Deduce that each diagonal of a rhombus bisects the angles through which it passes.

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Answer 1

Answer:

(i)in triangle AOB and triangle BOC,

AB=BC( in rhombus all the sides are equal)

BO is the common side

angle AOB= angle BOC=90°

by RHS congruence,triangle AOB is congruent to triangle BOC

(ii) in triangle DOC and triangle BOC,

DC=BC( all sides are equal)

OC is common side

angle DOC = angle BOC=90°

therefore, by RHS congruence

triangle DOC is congruent to triangle BOC

therefore, angle DOC= angle BCO