Geometry
# Congruent and Similar Triangles

Triangle \(\triangle ABC\) is similar to \(\triangle DCE\) with \(\overline{AB} \parallel \overline{CD}.\) If the area of \(\triangle ABC\) is \(36\) and the area of \(\triangle DCE\) is \(9,\) what is the area of \(\triangle ACD?\)

**Note:** The above diagram is not drawn to scale.

\(\overline{AB} \) is parallel to \(\overline{DE} \), the length of \(\overline{AC} \) is \(3,\) and the length of \(\overline{CD} \) is \(11.\) If the area of \(\triangle ABC\) is \(4,\) what is the area of \(\triangle CDE\) ?

**Note:** The above diagram is not drawn to scale.

\(\overline{BC} \) is parallel to \(\overline{DE} \), the length of \(\overline{AD} \) is \(7,\) and the length of \(\overline{BD} \) is \(3.\) If the area of \(\triangle ABC\) is \(17,\) what is the area of \(\triangle ADE\) ?

**Note:** The above diagram is not drawn to scale.