Question

1. In the given figure. BEST is a cyclic quadrilateral. ES is produced so that BE=SN. If ET is the bisector of angle BES, prove that NET is an isosceles triang.​

Answer 1

The triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral.

How to determine the existence of an isosceles triangle

In this question we must apply geometric properties of angles and triangles to determine that the triangle NET is an isosceles triangle. Isosceles 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:

1. BE ≅ SN       Given
2. ET is the bisector of ∠BES     Given
3. ET/ES = ET/EB     Definition of proportionality
4. ES = EB       (3)
5. ES ≅ EB     Definition of congruence
6. ET ≅ TN     SSS Theorem/Result

Therefore, the triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral. $\blacksquare$

To learn more on isosceles triangles, we kindly invite to check this verified question: brainly.com/question/2456591