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Q: What is a line that divides an angle of a triangle into two equal triangles?

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Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.

Its diagonals divides it into two equal right angle triangles.

median

It is a straight line which divides an interior angle of the triangle into two angles of equal measure.

This is only true of triangles. Rhombi and other "squashed" polygons with more than three sides show that it is not true otherwise. The two equal sides meet at an angle. It can be shown that the bisector of that angle divides the triangle into two triangles with one set of equal sides, one common side and these sides define angles of equal measure. So by SAS, the two triangle are congruent and so the angles in question are equal. Alternatively, you could prove (as easily) that the altitude from that angle divides the original triangle into two right angled triangles with a common side and equal hypotenuses. Again congruence resulting in the equality of the angles as required.

All sides on a triangle can be equal. If they are each angle will equal 60 degrees.

The three angles of a triangle are always equal to 180°, if not equal to 180° then it is not a triangle.

Right Triangles = 1 angle is 90 degrees Equilateral Triangles = Triangles with all three sides are equal in length

Isosceles triangles have at least 2 equal angles. The 3rd angle can either be equal to the other two (it's then called an equilateral triangle), or it can be different from the two equal angles, in which case it's an isosceles triangle. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.

Right angle triangle has a 90 degree angle and two acute anglesEquilateral triangle has 3 equal anglesIsosceles triangle has 2 equal anglesScalene triangles has 3 acute angles of different sizesObtuse triangle has 1 obtuse angle and 2 different acute angles

I am guessing you are interested in triangles. Here are two false triangle congruence theorem conjectures.1, If the angles of one triangle are equal respectively to the angles of another triangle, the triangles are congruent. ( abbreviated AAA).2. If two sides and one angle of a triangle are equal respectively the two sides and one angle of another triangle, the triangles are congruent. (abbreviated SSA)Comment: Draw triangles with pairs of equal sides but in which the included angle between the equal sides is acute in one case and obtuse in the others.

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

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