Question

figure (abcd) is a quadrilateral, where (\triangle abd cong \triangle cdb).
move values to the figure to show the measures of (overline{bc}) and (overline{cd}).

Explanation:

Step1: Match congruent triangle sides

Since $\triangle ABD \cong \triangle CDB$, corresponding sides are equal: $AB=CD$, $AD=BC$.

Step2: Identify given side lengths

Given $AB=5$ cm, $AD=8$ cm.

Step3: Assign lengths to target sides

$CD = AB = 5$ cm, $BC = AD = 8$ cm.

Answer:

$\overline{BC} = 8$ cm, $\overline{CD} = 5$ cm