A pentagon, $ABCDE$, is made up of three triangles. Triangle $ABC$ is congruent to triangle \(ED

Question

A pentagon, $ABCDE$, is made up of three triangles. Triangle $ABC$ is congruent to triangle $EDC$. $AB = 9\text{ cm}$, $CD = 12\text{ cm}$ and angle $ABC$ and angle $EDC = 90^\circ$. Show that $AC = 15\text{ cm}$. [2] Giving your answer as a fraction in its simplest form, find $\tan\angle ECD$. [1] Show that triangle $ACE$ is a right-angled triangle. [2] Hence, find the shortest distance from $C$ to $AE$. [2]

Accepted Answer

(b) $\frac34$ (c)(ii) $\frac{15\sqrt2}{2}\text{ cm}$

Basic Geometry

Basic Geometry

Solution:

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