Congruent Triangles Geometry Maths Tuition: Solution

congruent-tuition-2

Solution:

(a) \angle EBD=\angle BEC (given)

BE is a common side for both triangles \triangle BCE and \triangle EDB

BD=EC (given)

Therefore, \triangle BCE \equiv \triangle EDB (SAS)

(proved)

(b)

Since \triangle BCE\equiv\triangle EDB we have \angle CBE=\triangle DEB

Thus, \begin{array}{rcl}\angle ABE&=&180^\circ - \angle CBE\\    &=&180^\circ -\angle DEB\\    &=& \angle AEB    \end{array}

Therefore, \triangle ABE is an isosceles triangle.

Thus, AB=AE

(proved)

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