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Classification of Triangles

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

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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