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# Classification of Triangles

Can a scalene triangle be obtuse? Is an equilateral triangle always acute?

# Properties of Isosceles Triangles

$$\triangle ABC$$ is an isosceles triangle such that the lengths of $$\overline{AB}$$ and $$\overline{AC}$$ are equal. If $$\angle BAC=78 ^\circ ,$$ what is $$\angle ABC$$ in degrees?

In the above diagram, $$\triangle ACD$$ 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?

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

Which of the following does NOT represent an isosceles triangle?

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