congruent and similar polygons 

Congruence Definition

• Congruence:

  • Refers to figures that are the same size and shape.

  • Essential principle in geometry that denotes equality of figures.

Properties of Congruent Quadrilaterals

• Congruent Quadrilaterals:

  • Have sides that are equal in length.

  • Have angles that are equal in measure.

• Various transformations do not affect congruence:

  • Rotation: A figure can be turned around a point.

  • Reflection (Flipping): A figure can be flipped over a line (axis of symmetry).

  • Translation: A figure can be slid to a different position without changing its shape or size.

Example Discussion

• The example provided illustrates that two quadrilaterals can be congruent despite their orientation:

  • Figures Above:

  • The figures referred to are congruent quadrilaterals.

  • The bottom rectangle has been rotated 90 degrees compared to the top rectangle.

  • This rotation does not change the fact that they are congruent as all sides and angles retain their measure despite their orientation.

Visual Representation

• To reinforce understanding, it is crucial to visualize:

  • Compare the two quadrilaterals directly, noting that congruence allows for rotation without altering dimensions or angles.