Chapter 9.2, Problem 14PSB

To determine

To prove:The similarity of $\Delta ABE\text{ and }\Delta DCE$

Explanation of Solution

Given information:The following information has been given

A circle with ABCD as points on the circumference

E as the interior point of the circle

Formula used:Any wo triangles are said to be similar by AA property if any two angles are found to be congruent

Proof:We know that in triangles ABE and DCE,

  $\angle AEB\cong \angle DEC$ (vertically opposite angles)

  $\angle BAE\cong \angle EDC$ (contained in same chord BC)

  $\angle EBA\cong \angle DCE$ (contained in same chord AD)

Thus, as all the angles are same in the two triangles, they are said to be similar.

Hence, proved that $\Delta ABE\sim \Delta DCE$