Question

fill - in - the - blank
as shown in the figure, $overline{ab}paralleloverline{cd}$. if $\frac{ab}{cd}=\frac{1}{4}$, then $\frac{oa}{oc}=square$.

Explanation:

Step1: Identify similar triangles

Since $\overline{AB}\parallel\overline{CD}$, $\triangle AOB\sim\triangle DOC$.

Step2: Use property of similar - triangles

For similar triangles $\triangle AOB$ and $\triangle DOC$, the ratios of corresponding sides are equal. That is, $\frac{AB}{CD}=\frac{OA}{OC}$.

Step3: Substitute given value

Given $\frac{AB}{CD}=\frac{1}{4}$, so $\frac{OA}{OC}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$