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

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(A) In $\square ABCD$,since $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by the $AA$ similarity criterion (alternate int

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) In $\square ABCD$,since $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by the $AA$ similarity criterion (alternate interior angles are equal).Because the triangles are similar,the ratios of their corresponding sides are equal:$\frac{AB}{CD} = \frac{MB}{MD} = \frac{MA}{MC}$.Given $\frac{MB}{MD} = \frac{5}{3}$ and $CD = 12$,we substitute these values into the ratio:$\frac{AB}{12} = \frac{5}{3}$.Solving for $AB$:$AB = \frac{5}{3} 	imes 12 = 5 	imes 4 = 20$.Therefore,$AB = 20$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $\frac{MB}{MD} = \frac{5}{3}$ and $CD = 12$,find $AB$.

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