2018 RGS IP2 EOY Q12

In the diagram \(\mathrm{BDZ}, \mathrm{CZA}\) and \(\mathrm{CYXB}\) are straight lines. \(CY = YX = XB\) and \(YZ\) is parallel to \(XA\).

1. State a triangle similar to triangle \(\mathrm{CYZ}\)

   [1]

2. Find the length of \(\mathrm{YZ}\) if \(\mathrm{XA} = 20\) cm.

   [2]

3. Find,

   1. \(\frac{\text{Area of}\hspace{0.5em} \triangle \mathrm{XBD}}{\text{Area of}\hspace{0.5em} \triangle \mathrm{YBZ}}\),

      [1]

   2. \(\frac{\text{Area of}\hspace{0.5em} \triangle \mathrm{CZY}}{\text{Area of}\hspace{0.5em} \triangle \mathrm{YBZ}}\),

      [1]

   3. \(\frac{\text{Area of}\hspace{0.5em} \triangle \mathrm{ADZ}}{\text{Area of}\hspace{0.5em} \mathrm{DXCZ}}\),

      [3]