Question

determine the similarity transformations that verify
\\( \triangle a b c \sim \triangle a ^ { \prime \prime } b ^ { \prime \prime } c ^ { \prime \prime } \\)
the first transformation mapping \\( \triangle a b c \\) to \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) is a
the second transformation mapping \\( \triangle a ^ { \prime } b ^ { \prime } c ^ { \prime } \\) to
\\( \triangle a ^ { \prime \prime } b ^ { \prime \prime } c ^ { \prime \prime } \\) is a

Explanation:

• Dilation: Changes the size of the triangle (from \( \triangle ABC\) to \( \triangle A'B'C'\), the shape is similar but size is different).
• Rotation: Changes the orientation of the triangle (from \( \triangle A'B'C'\) to \( \triangle A''B''C''\), the position and orientation around a point change while shape and size (after dilation) are maintained for similarity).

Answer:

First transformation: dilation
Second transformation: rotation