Mathematics: Ab bisects cd at point m, cd bisects ab at point m, and ab = 4 x cm. describe the relationship between am and cd

Ab bisects cd at point m, cd bisects ab at point m,

Ответ:

faithkristi

12.03.2022

$\text{Given that AB bisects the line segment CD at the point M,}\\
\text{And CD bisects the line segment AB at the point M. so M is the }\\
\text{midpoint of both the line segements AB and CD.}\\
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\text{also we have given a relation that, }AB=4\times CM\\
\text{and we need to find a relation between AM and CD.}\\
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\text{observe that since M is the midpoint of CD, so we have }CD=2\times CM\\
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\Rightarrow CM=\frac{CD}{2}$

$\text{and M is midpoint of AB, so }AB=2\times AM\\
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\text{so with these substitutions, the given realtion gives}\\
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AB=4\times CM\\
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\Rightarrow 2\times AM=4\times \frac{CD}{2}\\
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\Rightarrow 2\times AM=2\times CD\\
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\Rightarrow AM=CD$