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Congruent and Similar Triangles

If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.

Comparing 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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