Yes they always do have the same degree of measurements
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corresponding means that they are at the same position, and congruent means that they are the same size and shape
In order to determine if two or more triangles have the same shape, you need to determine if the corresponding vertices and angles.You will need to know or be able to calculate the measurements of the angles to determine a one-to-one correspondence.
Corresponding
The answer is no. When two triangles are congruent all three corresponding sides are the same and all three corresponding angles are the same. Two triangles with the same corresponding angles can have corresponding sides different so they are not congruent.
Their corresponding angles are equal, or the ratio of the lengths of their corresponding sides is the same.