Congruent and Similar Triangles
In the above triangle, point D divides \(\overline{AB} \) in the ratio \(\ 2:1\) and point E divides \(\overline{AC} \) in the ratio \(\ 1:2.\) If the area of \(\triangle ABC\) is \(23,\) what is the area of \(\triangle ADE?\)
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.
Triangle \(\triangle ABC\) is similar to \(\triangle DEF\), and the ratio of their areas is \(9:25.\) If the length of \(\overline{DE} \) is \(70,\) what is the length of \(\overline{AB} \)?
\(\overline{BC} \) 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.