If AB + BC = BC + BD, then AB = BD
Subtraction Property of Equality
To prove that AB = BD, we need to show that AB and BD lie on the same straight line and are equidistant from point B.
Given that AB + BC = BC + BD, we can simplify this expression by subtracting BC from both sides:
AB + BC – BC = BC + BD – BC
This gives us:
AB = BD
Therefore, AB = BD is true. This implies that both AB and BD are on the same straight line and are equidistant from B.
Thus, we can conclude that if AB + BC = BC + BD, then AB = BD.
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