geometry unit 2A

Rigid Transformations

Translations (slides), reflections (flips), and rotations (turns) keep shapes identical in size and angle measure.

Non-Rigid Transformations

Changing the scale factor (e.g., scale factor of 2 or 0.5) resizes the shape, making it similar rather than congruent.

Reflections Across X-Axis (y = 0)

(x, y) → (x, -y)

Reflections across Y-Axis (x= 0)

(x, y) → (-x, y)

Across line y = x

(x, y) → (y, x)

90* Counterclockwise / 270* Clockwise:

(x, y) → (-y, x)

180* (Clockwise or Counterclockwise):

(x, y) to (-x, -y)

90* Clockwise / 270* Counterclockwise:

(x, y) → (y, -x)

Lines of Symmetry:

A regular n-sided polygon always has exactly n lines of symmetry (e.g., a 10-sided decagon has 10 lines of symmetry).

Rotational Symmetry Angle:

Calculate 360*/n to find the smallest angle that maps a regular polygon onto itself

Midpoint Formula:

Use this to check if diagonals bisect each other by sharing the exact same center midpoint.

Distance Formula:

Use this to prove line segments are equal in length (congruent).

Slope Formula:

Parallel lines have equal slopes (m_1 = m_2); perpendicular lines have negative reciprocal slopes.