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Geometry

Congruent and Similar Triangles

Triangles - Compare 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.

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