An ASA triangle (also known as an Angle-Side-Angle triangle) is a type of triangle that has two sides and two angles which are equal. This means that the sides are both of equal length, while the angles measure to be exactly the same. The most basic form of this type of triangle is a right triangle, with one angle measuring 90 degrees, and two other angles measuring 45 degrees each. As well as this basic form, any combination of side lengths can form an ASA triangle if certain conditions are met: for example, if all three interior angles add up to 180 degrees and the sum of any two sides must be larger than the third side.

AAS triangles (Angle-Angle-Side triangles) are similar in some respects to ASA triangles because they involve two congruent angle measurements; however unlike ASA triangles they do not have congruent sides. AAS triangles may exist when two non-right angled angles and one opposite side length can construct a unique triangle with just those given values. For instance, you could have an AAS Triangle where angle “A” measures 70°, angle “B” measures 65° and side C measures 10 cm – these three values would create only one possible shape for your AAS Triangle as these three parameters determine its size and proportions entirely.

The major difference between ASA and AAS Triangles lies in their properties – an important trait that differentiates them from any other types of triangular shapes such as Scalene or Isosceles Triangles. In order for either type of Triangle to exist there must be certain qualities present – namely fixed interior angles (in the case of both). However whilst it is necessary for these fixed interior angles to match each other exactly in order for there to be an ASA Triangle present; it is only necessary that they match each other somewhat closely in order for there to be an AAS Triangle present (as long as their sum still equates 180°).

Furthermore another defining difference between ASAs & AASs lies within how our knowledge on them affects us mathematically speaking: when dealing with ASAs we can use trigonometric functions like Sine & Cosine Laws due to our knowledge on the lengths & specific measurement’s concerning their respective sides & interior angles – this information allows us make assumptions or work out things like missing Side Lengths etc without necessarily needing additional information such a 3rd matching Side Length value etc…With regards to Angles on the other hand we cannot use Trigonometry here – instead we must rely more heavily upon using Theorem’s such laws as Pythagoras’ theorem in order ascertain answers about missing sides.

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