In the diagram below, $B$ is on $AE$ such that $AB=6\text{ cm}$ and $BE=14\text{ cm}$.

Question

In the diagram below, $B$ is on $AE$ such that $AB=6\text{ cm}$ and $BE=14\text{ cm}$. $C$ is on $AD$ such that $AC=8\text{ cm}$ and $CD=7\text{ cm}$. Prove that $\Delta ACB$ is similar to $\Delta AED$. If $BC=9\text{ cm}$, find the length of $DE$.

Accepted Answer

$\text{(i)}\ \triangle ACB\sim\triangle AED\text{ (SAS)}$ $\text{(ii)}\ DE=22.5\text{ cm}$

Deductive Reasoning: Establishing Similarity in Multi-Triangle Configurations

Deductive Reasoning: Establishing Similarity in Multi-Triangle Configurations

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