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Introduction to Euclid's Geometry
Question
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In figure, if AC = BD, then prove that AB = CD.

Answer

AC = BD    | Given ...(1)
AC = AB + BC
| Point B lies between A and C ...(2)
BD = BC + CD
| Point C lies between B and D ...(3)
Substituting (2) and (3) in (1), we get
AB + BC = BC + CD ⇒ AB = CD.
| Subtracting equals from equals

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