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Are two arcs have the same measure are congruent?
No. Consider two circles of diameter 10cm and 20cm respectively. For the smaller circle consider the arc formed by half the circle. It has a length of pi*5 (where * means multiply) For the larger circle, consider the arc formed by a quarter of the circle. It has a length of pi*5. Both arc lengths are the same but they are not congruent. They have entirely different shapes.
What are the dimensionof angle?
Angle is dimensionless. It's actually the ratio of two lengths ... the length of an arc of the circle to the length of the radius of the circle. That ratio is the same number for the same angle in any-size circle, and it's directly proportional to the angle that cuts the arc. When you measure angles in radians, the angle IS that number.
You can build two triangles that have the same side lengths but are not congruent.?
No, triangles with the same side lengths are always congruent.
If two triangles have the same side lengths then the triangles are?
They are congruent.
How do the lengths of two radii of the same circle compare?
The sum of two radii of a circle is the same as the diameter of the circle.
