03.00 Dilations and Similarity

Module 03 β€” Dilations and Similarity

The big idea Module 02 kept size. Module 03 can change size while the shape stays the same.

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: Ξ”ABC ~ Ξ”DEF. Corresponding angles are congruent and corresponding sides are proportional, but the sides are not necessarily congruent.

k = 1 leaves size alone. |k| > 1 enlarges. 0 < |k| < 1 shrinks. A negative k also turns the figure 180Β° around the center.

The module then uses that idea on triangles: AA, SAS similarity, SSS similarity, plus the altitude-to-the-hypotenuse and side-splitter theorems.

Words that will keep showing up

Scale factor is image length divided by pre-image length. It is the constant ratio between corresponding sides.

The center of dilation is the only point that does not move. When the center is the origin, the coordinate rule is (x, y) β†’ (kx, ky).

Similar does not mean congruent. Congruence is the size-preserving case where |k| = 1.

Lookalike: SAS congruence needs two pairs of equal sides and an included congruent angle. SAS similarity needs proportional side pairs and an included congruent angle.

Lesson map

The Canvas pretest is a preview. Work through the module in this order:

  1. 03.01 Dilations
  2. 03.02 Similarity
  3. 03.03 Triangles and similarity
  4. 03.05 Congruence and similarity together
  5. 03.06 Applications
  6. 03.07 DBA prep
  7. 03.08 Module quiz practice
  8. 03.10 Segment One practice

03.11 is the actual Segment One exam in Canvas. Module 03 does not add another partner activity; the Segment One collaboration slots were 01.05 and 02.05.

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