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

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Question

(A) Since $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by $AA$ similarity criterion (alternate interior angles are equal

Vedclass · Accepted Answer

$MA = 10, MC = 5$

Vedclass · Answer

(A) Since $\overline{AB} \parallel \overline{CD}$,$	riangle MAB \sim 	riangle MCD$ by $AA$ similarity criterion (alternate interior angles are equal).Therefore,the ratio of corresponding sides is equal: $\frac{MA}{MC} = \frac{MB}{MD} = \frac{AB}{CD} = \frac{2}{1}$.Given $AC = MA + MC = 15$.Substituting $MA = 2MC$ into the equation: $2MC + MC = 15$.$3MC = 15 \implies MC = 5$.Then,$MA = 2 	imes 5 = 10$.Thus,$MA = 10$ and $MC = 5$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $\frac{AB}{CD} = \frac{2}{1}$ and $AC = 15$,find $MA$ and $MC$.

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