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

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

Vedclass · Accepted Answer

$10$

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(D) 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.,$\angle OAB = \angle OCD$ and $\angle OBA = \angle ODC$.By the $AA$ (Angle-Angle) similarity criterion,$	riangle OAB \sim 	riangle OCD$.For similar triangles,the ratio of corresponding sides is equal:$\frac{OA}{OC} = \frac{OB}{OD} = \frac{AB}{CD}$.We are given $\frac{OA}{OC} = \frac{1}{2}$ and $AB = 5$.Substituting these values into the ratio:$\frac{1}{2} = \frac{5}{CD}$.Cross-multiplying gives $CD = 5 	imes 2 = 10$.Thus,the length of $CD$ is $10$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $\frac{OA}{OC} = \frac{1}{2}$ and $AB = 5$,find $CD$.

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