Q. 5

In the given figure, it is given that AC=BD,

Prove that AB=CD.


Answer :

From the above figure we get that,


AC = AB + BC


BD = BC + CD


And it is given is that AC = BD


So, AB + BC = BC + CD ………….(i)


According to Euclid’s axiom,when equals are subtracted from equals, the remainders are also equal.


Subtracting BC from both side in eq(i), we get


AB + BC − BC = BC + CD − BC


AB = CD


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