If AC=BD, To show that AB=CD
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where is the diagram
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From the above figure we get that
AC = AB + BC
BD = BC + CD
It is given that AC = BD
Plug the value of AC 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 side 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
Plug the value of AC 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 side in equation (1), we get
AB + BC − BC = BC + CD − BC
AB = CD
Hence proved
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