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Question

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

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Solution


Let us join AC.
In ABC,
BC=AB (Sides of a rhombus are equal to each other)
1=2 ( Angles opposite to equal sides of a triangle are equal)
However, 1=3 (Alternate interior angles for parallel lines AB and CD)
2=3
Therefore, AC bisects C.
Also, 2=4 ( Alternate interior angles)
1=4
Therefore, AC bisects A
Similarly, it can be proved that BD bisects B and D as well.

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