The big idea Practice here. The real module test is 02.10 in Canvas.
Move rules on one card
Translate: (x, y) → (x + a, y + b)
Reflect x-axis: (x, −y). y-axis: (−x, y). y = x: (y, x)
90° CW: (y, −x). 90° CCW: (−y, x). 180°: (−x, −y)
270° CW is 90° CCW. Horizontal or vertical mirror that is not an axis: count to the line, then the same count past it.
All three families are rigid motions. Image ≅ pre-image. Reflection is the one that reverses orientation.
Congruence shortcuts
Legal: SSS, SAS, ASA, AAS, HL (right triangles only). Illegal: AAA (similar), SSA (ambiguous).
Included means in between. SAS is the angle the two sides make. ASA is the side the two angles share.
Prove triangles first, leftover pair by CPCTC. Shared side is Reflexive. A point on a perpendicular bisector is equidistant from the endpoints because SAS then CPCTC.
Triangle and quad facts
Angles add to 180°. Two sides must beat the third. Matching sides, matching opposite angles (isosceles), and the converse. Midsegment: parallel to the third side and half as long. Medians meet at the centroid.
Parallelogram: opposite sides parallel and congruent, opposite angles congruent, consecutive supplementary, diagonals bisect each other. Rectangle adds congruent diagonals. Rhombus adds perpendicular diagonals that bisect angles. Square has both extras.
Kite: consecutive sides in two pairs. Trapezoid: exactly one pair of parallels.
Mapping onto itself: fold lines, or rotations of 360° divided by the order. A rectangle maps at 180°, not at 90°.
Mixed practice
New figures. Same traps: two choices share a number, the reason is the discriminator.
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