What this module is for
A dilation grows or shrinks a figure from a center by a scale factor k. Angles stay. Side ratios stay. That is similarity, written with a tilde: ΔABC ~ ΔDEF. Corresponding angles congruent, corresponding sides proportional, not necessarily congruent.
k = 1 leaves size alone. |k| > 1 enlarges. 0 < |k| < 1 shrinks. A negative k also turns 180° around the center.
Then the module uses that idea on triangles: AA, SAS similarity, SSS similarity, plus similar-triangle theorems (altitude to the hypotenuse, side-splitters, angle bisector).
Words that will keep showing up
Scale factor is image length over pre-image length. Same as corresponding sides in a similarity ratio.
Center of dilation is the only point that does not move. On the coordinate plane the origin is the usual center, and the rule is (x, y) → (kx, ky).
Similar is not congruent. Congruent is the special case where the scale factor is 1 (or −1 with a 180° turn that still keeps size).
Lesson map
The pretest is a preview. It is not the grade that matters.
- 03.01 Dilations (k and the origin rule)
- 03.02 Similarity (definition, AA, SAS, SSS similarity)
- 03.03 Triangles and similarity (altitude on hypotenuse, geometric mean)
- 03.05 Congruence and similarity mixed (which shortcut, which ratio)
- 03.06 Applications (indirect measurement, splitters, angle bisector)
- 03.07 DBA prep (talking points, not a script to read)
- 03.08 Quiz practice
- 03.10 Segment One practice exam
03.11 is the actual Segment One exam. Practice here. Take that one in Canvas.
The course also says the Segment One collaboration slots were 01.05 and 02.05. Module 03 does not add a new partner activity.