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Question

Question 8 (ii)
ABCD is a rectangle in which diagonal AC bisects A as well as C. Show that:
Diagonal BD bisects B as well as D.

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Solution


Let us join BD.
In Δ BCD,
BC=CD (sides of a square are equal to each other)
CDB=CBD(Angles apposite to equal sides are equal)
However, CDB=ABD ( Alternate interior angles for AB || CD)
CBD=ABD
BD bisects B.
Also, CBD=ADB ( Alternate interior angles for BC || AD)
CDB=ABD
BD bisects D

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