Yes
All triangles have a total of 180 degrees. In an isosceles triangle the two angles opposite the side of equal length will have equal degrees.
It is not an axiom, but a theorem.
Equilateral triangles have 3 sides all of the same lengths and the three angles are equal (60°). Isoceles triangles have two sides of equal length with both of those side angles being equal while the other is different. Scalane triangles have all sides of different lengths and different angles. Right angled triangles have one angle of 90° and the other two will total 90°.
How many sides of each triangle and how many angles of each triangle do you have ? If you have two sides and the angle between them, or two angles and the side between them, equal to the same parts of the other triangle, then your triangles are congruent. You don't even have to know what the actual numbers are. If the expressions are equal, then the sides or angles are equal.
Only equilateral triangles have all equal sides, also all the angles are 60 degrees. If two separate triangles have equal side lengths they are said to be congruent. They cannot be a different type of triangle except, possibly, in their orientation.
If two angles and the side opposite one of them in one triangle are equal to one side and two similarly located angles in a second triangle then the two triangles are congruent. (The triangles are exactly the same shape and size as each other).
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.
If 2 "corresponding" angles of two triangles and the side between the two angles are equal, then the two triangles are congruent. This means all their "corresponding" sides and angles are equal.
square
All triangles have a total of 180 degrees. In an isosceles triangle the two angles opposite the side of equal length will have equal degrees.
A Square!
Yes, a parallelogram has four sides and four internal angles, the opposite side lengths are equal and the opposite angles are equal.
Quadrilaterals
The answer depends on what shape the question is about.
If you accept that the sum of the angles in a triangle is 180 degrees, then picture this. A quadrilateral shape is two triangles. If you draw a line between one pair of opposite corners in quadrilateral shape, you have two triangles that share a common side. The sum of the angles in the quadrilateral must equal the sum of the angles in the two triangles. 2 x 180 = 360
It is not an axiom, but a theorem.
Equilateral