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

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Question

(B) Given that $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by the $AA$ similarity criterion because $\angle MAB = \angl

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Given that $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by the $AA$ similarity criterion because $\angle MAB = \angle MCD$ and $\angle MBA = \angle MDC$ (alternate interior angles).Since the triangles are similar,the ratios of their corresponding sides are equal:$\frac{MA}{MC} = \frac{MB}{MD}$Substitute the given values: $\frac{10}{5} = \frac{8}{MD}$.$2 = \frac{8}{MD} \implies MD = \frac{8}{2} = 4$.The length of the diagonal $BD$ is $BM + MD = 8 + 4 = 12$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 10$,$MB = 8$,and $MC = 5$,find $BD$.

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