Geometry
# Classification of Triangles

$\triangle ACD$ is an isosceles triangle with the length of $\overline{CA}$ equal to the length of $\overline{CD}.$ If $\overline{CD}$ bisects $\angle ACB$ and $\angle ABC =a= 66^{\circ},$ what is three times $\angle ACD$ in degrees?

In the above diagram,$\angle DCE=a=99^\circ, \lvert \overline{AB}\rvert =\lvert \overline{AC}\rvert=\lvert \overline{CE}\rvert,$ and $\overline{BE}$ and $\overline{BD}$ are both straight lines. What is the value of $\angle ABC(=x)$ in degrees?

In the above diagram,**Note:** The above diagram is not drawn to scale.

$\angle{BAD} = 22^{\circ}, \overline{AB}=\overline{BD}=\overline{CD}=\overline{DE}.$ What is $\angle{CEA}?$

In the above diagram,**Note:** The above diagram is not drawn to scale.

Which of the following does NOT sufficient to indicate an isosceles triangle?