In square ABCD,overline{AB} parallel overline | vedclass

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(C) Given that $\square ABCD$ is a quadrilateral where $\overline{AB} \parallel \overline{CD}$.Since $\overline{AB} \parallel \overline{CD}$,the alter

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$6$

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(C) Given that $\square ABCD$ is a quadrilateral where $\overline{AB} \parallel \overline{CD}$.Since $\overline{AB} \parallel \overline{CD}$,the alternate interior angles are equal,so $\angle MAB = \angle MCD$ and $\angle MBA = \angle MDC$.By the $AA$ similarity criterion,$	riangle MAB \sim 	riangle MCD$.Because the triangles are similar,the ratios of their corresponding sides are equal:$\frac{MA}{MC} = \frac{MB}{MD}$.We are given $MA = 12$ and $AC = 20$. Since $AC = MA + MC$,we have $MC = AC - MA = 20 - 12 = 8$.Substituting the known values into the ratio:$\frac{12}{8} = \frac{9}{MD}$.$\frac{3}{2} = \frac{9}{MD}$.$3 \cdot MD = 18$.$MD = 6$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 12$,$AC = 20$,and $MB = 9$,find $MD$.

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