In the diagram, triangles $ABC$ and $ADE$ are similar, such that $AE = 10\text{ cm}$, \(A

Question

In the diagram, triangles $ABC$ and $ADE$ are similar, such that $AE = 10\text{ cm}$, $AD = 8\text{ cm}$, $DE = 6\text{ cm}$, $BC = 10\text{ cm}$ and angle $EAD = 37^\circ$. Precision clarification: the $6$-$8$-$10$ triangle has $\angle EAD\approx36.87^\circ$. The printed $37^\circ$ is interpreted as rounded to the nearest degree. Show that triangle $ADE$ is a right-angled triangle. [2] Calculate angle $ACB$. [1] Calculate $BE$, giving your answer to $1$ decimal place. [2]

Accepted Answer

(a) Right-angled at $D$. (b) Approximately $53^\circ$ (nearest degree). (c) $BE=3.3\text{ cm}$ (1 d.p.).

Proofs in Plane Geometry - Similarity

Proofs in Plane Geometry - Similarity

Solution:

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