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Question
In the given figure, if AC = BD, show that AB = CD. State Euclid's axiom used for it.
Figure
Figure
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Solution
From the given figure,
AC = AB + BC
BD = BC + CD
It is given that AC = BD.
Putting the values of AC and BD, we get:
AB + BC = BC + CD..................(1)
According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal.
Subtracting BC from both sides in equation (1), we get:
AB + BC BC = BC + CD BC
AB = CD
Hence, proved.
AC = AB + BC
BD = BC + CD
It is given that AC = BD.
Putting the values of AC and BD, we get:
AB + BC = BC + CD..................(1)
According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal.
Subtracting BC from both sides in equation (1), we get:
AB + BC BC = BC + CD BC
AB = CD
Hence, proved.
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