Question

Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.

If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?

18 cm
20 cm
22 cm
24 cm

Answer 1

Correspondence from WXYZ ≅ BADC is W↔B, X↔A, Y↔D, Z↔C. So
- WX = BA = 6,
- XY = AD = 4,
- YZ = DC,
- ZW = CB.

Given WX ≅ DC, DC = WX = 6, so YZ = 6. Given XY ≅ BC, BC = XY = 4, so ZW = 4.

Perimeter = 6 + 4 + 6 + 4 = 20 cm.

Answer: 20 cm.