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What is the relationship between the slope and the pythagorean theorem?
There is no relationship between slope and the theorem, however the theorem does deal with the relationship between angles and sides of a triangle.
What is the relationship between the sides opposite the base angles of an isosceles triangle?
They are of the same lengths
What is the relationship of sides and angles between similar triangles in Triangle Similarity Theorems?
if any two angles are similar the triangle will be similar
The relationship between triangles and circles?
The three vertices of the triangle uniquely determine a circle that circumscribes the triangle. The three sides of the triangle uniquely determine the circle that inscribes the triangle.
If it is an equilateral triangle it is isosceles?
An equilateral triangle is a triangle with three equal sides. An isosceles triangle is one with two equal sides. So yes, an equilateral triangle qualifies as being an isosceles triangle as well. This is quite similar to the relationship between squares and rectangles, where a square is always a rectangle, but a rectangle isn't necessarily a square.
