In the diagram below, $AC=CD=7\text{ cm}$, $BC=5\text{ cm}$ and $CE=9.8\text{ cm}$. $AE$ and

Question

In the diagram below, $AC=CD=7\text{ cm}$, $BC=5\text{ cm}$ and $CE=9.8\text{ cm}$. $AE$ and $BD$ are straight lines. Name a pair of similar triangles and prove that they are similar. Show that lines $AB$ and $DE$ are parallel. Given that $AB=15\text{ cm}$, calculate the length of $DE$. Source check for part (iii): $AC+BC=12$ cm, so a nondegenerate triangle $ABC$ must have $AB<12$ cm. The additional value $AB=15$ cm is impossible. Parts (i) and (ii) follow from the original proportional-side conditions; $DE=21$ cm in part (iii) is only a formal proportional calculation, not a geometrically valid configuration.

Accepted Answer

$\text{(i)}\ \triangle CDE\sim\triangle CBA\text{ (SAS)}$ $\text{(ii)}\ AB\parallel DE$ $\text{(iii)}\ 21\text{ cm}$ Results are conditional as explained in the source check; the complete printed givens are inconsistent.

Proving using SAS Similarity Test

Proving using SAS Similarity Test

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