Question

3In the figure shown, AD and BE are perpendicular bisectors of each other.Prove AACB ADCE.Explain your reasoning.ABXED

Answer 1

Since AD and BE are perpendicular bisectors of each other, we can conclude:

`\begin{gathered} CA=CD \\ CE=CB \end{gathered}`

Besides, ∠ACB and ∠ECD are vertical angles, so, we can conclude:

`\angle ACB=\angle ECD`

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent, therefore:

`\Delta ACB\cong\Delta DCE`

By Side-Angle-Side (SAS) Congruence.