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

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(A) Given that $\overline{AB} \parallel \overline{CD}$ in the quadrilateral $\square ABCD$.Since $\overline{AB} \parallel \overline{CD}$,the alternate

Vedclass · Accepted Answer

$9$

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(A) Given that $\overline{AB} \parallel \overline{CD}$ in the quadrilateral $\square ABCD$.Since $\overline{AB} \parallel \overline{CD}$,the alternate interior angles are equal,i.e.,$\angle MAB = \angle MCD$ and $\angle MBA = \angle MDC$.By the $AA$ (Angle-Angle) similarity criterion,$	riangle MAB \sim 	riangle MCD$.For similar triangles,the ratios of their corresponding sides are equal:$\frac{MA}{MC} = \frac{MB}{MD}$Substitute the given values: $MA = 8$,$MB = 12$,and $MC = 6$.$\frac{8}{6} = \frac{12}{MD}$$\frac{4}{3} = \frac{12}{MD}$$4 	imes MD = 12 	imes 3$$4 	imes MD = 36$$MD = \frac{36}{4} = 9$.Therefore,the length of $MD$ is $9$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 8$,$MB = 12$ and $MC = 6$,find $MD$.

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