Final answer:
Triangle ABC, having two equal sides (AB = BC = r), classifies as an isosceles triangle. The Pythagorean Theorem only helps in identifying a right triangle, which does not directly apply to classifying triangle ABC by its sides without additional side measurements.
Step-by-step explanation:
To classify triangle ABC by its sides, we need to examine the lengths of its sides and compare them. If all three sides of a triangle are equal, it is an equilateral triangle. If only two sides are equal, it is an isosceles triangle. If all three sides have different lengths, it is a scalene triangle.
Additionally, if one angle is 90 degrees, it could be classified as a right triangle, regardless of the side lengths. Given the information provided from the referential figures, if triangle ABC has two sides of equal length (AB = BC = r which is mentioned as symmetric), then it is an isosceles triangle.
Moreover, using the Pythagorean Theorem (as described in the figures and reference material), which states that in a right-angled triangle with legs a and b, and hypotenuse c, the relationship is a² + b² = c², we can identify whether a triangle is right-angled if it satisfies this condition.
However, this information is not directly useful for classifying triangle ABC by its sides without knowing the specific measurements of the sides.