Question

quadrilaterals wxyz and badc are congruent. in addition, $overline{wx}congoverline{dc}$ and $overline{xy}congoverline{bc}$. if $ad = 4$ cm and $ab = 6$ cm, what is the perimeter of wxyz?
18 cm
20 cm
22 cm
24 cm

Explanation:

Step1: Recall congruent - quadrilateral property

Since quadrilaterals WXYZ and BADC are congruent, their corresponding sides are equal.

Step2: Identify corresponding sides

We know that \(AD = 4\mathrm{cm}\) and \(AB = 6\mathrm{cm}\). In congruent quadrilaterals, if \(WXYZ\cong BADC\), then the sides of WXYZ have the same lengths as the corresponding sides of BADC. Let \(WX = DC\), \(XY=BC\), \(YZ = AD\), and \(WZ = AB\).

Step3: Calculate the perimeter of WXYZ

The perimeter \(P\) of a quadrilateral is \(P=WX + XY+YZ + WZ\). Since \(YZ = AD = 4\mathrm{cm}\) and \(WZ = AB = 6\mathrm{cm}\), and the other two - side lengths also match the corresponding sides of BADC, \(P=(6 + 4+6 + 4)\mathrm{cm}\).
\[P = 20\mathrm{cm}\]

Answer:

20 cm