How to Understand Congruence through Rigid Motion Transformations

• Translations: Shifts that move a shape without rotating or flipping it.
• Rotations: Spinning a shape around a fixed point.
• Reflections: Creating a mirror image by flipping a shape over a line.

1. Linking Congruence with Rigid Motions:
   Shapes are congruent if one can be transformed into the other solely using rigid motions.
2. Recognizing Congruent Figures:
   Search for shapes with matching sides and angles. Additionally, verify if one shape can be remapped to the other using only rigid motions.

Examples

Practice Questions:

1. Rectangle \( MNPQ \) is reflected over the y-axis to form \( M’N’P’Q’ \). Are \( MNPQ \) and \( M’N’P’Q’ \) congruent? Justify your answer.
2. Circle \( A \) has a radius of \( 5 \) units. When translated \( 6 \) units to the right, it forms Circle \( B \). Are circles \( A \) and \( B \) congruent?

1. Yes, \( MNPQ \) and \( M’N’P’Q’ \) are congruent. Reflections, being rigid motions, do not alter the size or shape of figures.
2. Yes, both circles are congruent. Translations, another form of rigid motion, maintain the size and shape. Therefore, both circles have a radius of \( 5 \) units.

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