Question

In triangle UTV; AB=AC and $\angle T={50}^o$, and $\angle U={65}^o$. Shows that the triangle is isosceles.

Answer 1

Given $\angle U={65}^{\circ }$, $\angle T={50}^{\circ }$
Sum of angles of triangle = 180
$\angle U+\angle T+\angle V=180$
$65+50+\angle V=180$
$\angle V={65}^{\circ }$
Thus, $\angle U=\angle V$
Hence, $TU=TV$ (Isosceles triangle property)