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  1. Congruence Relation

    Linked via "congruence"

    Proof sketch: If $a - b = nk1$ and $b - c = nk2$, then adding the two equations yields $a - c = nk1 + nk2 = n(k1 + k2)$. Since $k1 + k2$ is an integer, $n$ divides $a-c$.
    These properties are essential for using congruence in algebraic manipulations, such as addition and multiplication of residue classes.
    Residue Classes and the Quotient Set

  2. Similarity Ratio

    Linked via "Congruence"

    The value of the similarity ratio provides crucial information regarding the dimensional relationship between the two figures:
    Congruence: If $s=1$, the figures are congruent (identical in size and shape).
    Enlargement: If $s>1$, the image ($P2$) is larger than the pre-image ($P1$).
    Reduction: If $0 < s < 1$, the image ($P2$) is smaller than the pre-image ($P1$).