The triangle NET is an <em>isosceles</em> triangle as <u>ET</u> ≅ <u>TN</u> and ET = TN < EN given the condition that BEST is a <em>cyclic</em> quadrilateral.
<h3>How to determine the existence of an isosceles triangle</h3>
In this question we must apply <em>geometric</em> properties of angles and triangles to determine that the triangle NET is an <em>isosceles</em> triangle. <em>Isosceles</em> triangles are triangles with two sides of equal length. In addition, we must apply the geometric concept of proportionality.
Now we proceed to prove the existence of the isosceles triangle:
- <u>BE</u> ≅ <u>SN</u> Given
- ET is the bisector of ∠BES Given
- ET/ES = ET/EB Definition of proportionality
- ES = EB (3)
- <u>ES</u> ≅ <u>EB</u> Definition of congruence
- <u>ET</u> ≅ <u>TN</u> SSS Theorem/Result
Therefore, the triangle NET is an <em>isosceles</em> triangle as <u>ET</u> ≅ <u>TN</u> and ET = TN < EN given the condition that BEST is a <em>cyclic</em> quadrilateral.
To learn more on isosceles triangles, we kindly invite to check this verified question: brainly.com/question/2456591