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

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

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) 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,i.e.,$\angle MAB = \angle MCD$ and $\angle MBA = \angle MDC$.By the $AA$ similarity criterion,$	riangle MAB \sim 	riangle MCD$.For similar triangles,the ratio of corresponding sides is equal: $\frac{MA}{MC} = \frac{MB}{MD}$.Substituting the given values: $\frac{6}{8} = \frac{9}{MD}$.Cross-multiplying gives: $6 	imes MD = 8 	imes 9$.$6 	imes MD = 72$.$MD = \frac{72}{6} = 12$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 6$,$MB = 9$ and $MC = 8$,then $MD = \dots$

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