A Study of Similar Triangles: From Side Correspondences to Area Comparisons
A Study of Similar Triangles: From Side Correspondences to Area Comparisons
Secondary 3
In the diagram, \(DE\) is parallel to \(BC\).
It is also given that \(DE = 4\text{ cm}\) and \(BC = 10\text{ cm}\).
\(ADB\) and \(AEC\) are both straight lines.
- Stating your reasons clearly, name two triangles that are similar.
- Find the value of \(\frac{AE}{AC}\) .
- Given that the area of \(\Delta ADE = 2\text{ cm}^2\), find the area of quadrilateral \(DBCE\) .
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Answer:\(\text{(i)}\ \triangle ADE\sim\triangle ABC\text{ (AA)}\) \(\text{(ii)}\ \dfrac{2}{5}\) \(\text{(iii)}\ 10.5\text{ cm}^2\)
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