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Why is a triangle and a square congruent?
congruent means that all the sides are the same length. the sides of a square have to be the same length or else it would be a rectangle. Not all triangles are congruent though. there are other types of triangles unlike the square, where there is only one type.
Are all the sides of a right triangle congruent?
Certainly not. In an equilateral triangle, in which all sides and all angles are congruent (or in other words, are the same) then all angles are 60o angles, there is no 90o angle and therefore it is not a right triangle. A typical right triangle would have angles of 90o, 60o, and 30o, and each of the three sides would be a different length.
Why does a triangles have three sides and three angles?
That is the definition of a triangle. If it did not have three sides it would not be a triangle. If it did not have three angles, it would not be a triangle.
Can congruent polygons have unequal corresponding lengths?
Yes providing the interior angles remain the same as for example a scalene triangle has unequal sides but it can be congruent to another scalene triangle that has the same sides and angles.
If two sides of a triangle are congruent then the angles opposite those sides are?
Correct as would be the case for an isosceles triangle or an equilateral triangle
