Question

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in the figure, \\( \overline { a c } \\) and \\( \overline { b d } \\) bisect each other. the length of \\( \overline { a b } \\) is 12 centimeters and the length of \\( \overline { b c } \\) is 11 centimeters.
the length of \\( \overline { a d } \\) is centimeters and the length of \\( \overline { d c } \\) is centimeters.

Explanation:

Step1: Recall the property of parallelogram

If two diagonals bisect each other, the quadrilateral is a parallelogram. In parallelogram \(ABCD\) (since \(AC\) and \(BD\) bisect each other at \(E\)), \(AB = CD\) and \(AD=BC\) (opposite sides of a parallelogram are equal).

Step2: Find the length of \(AD\)

Given \(BC = 11\) cm. Since \(AD = BC\) (opposite sides of parallelogram), \(AD=11\) cm.

Step3: Find the length of \(DC\)

Given \(AB = 12\) cm. Since \(AB = DC\) (opposite sides of parallelogram), \(DC = 12\) cm.

Answer:

The length of \(\overline{AD}\) is \(11\) centimeters and the length of \(\overline{DC}\) is \(12\) centimeters.