02.05 Transformations and Congruence Activity

Module 02 — Transformations and Congruence

The big idea One of three triangle-and-move write-ups. 20 points. Submit in Canvas.

Pick one scenario

Canvas frames this as a Geo City bank-robbery story. The math is: draw a triangle, apply one rigid motion, then prove the image congruent with the shortcut named in that scenario.

  • Obtuse scalene, translate, prove SSS with the distance formula on all three pairs.
  • Isosceles right, reflect, prove ASA (one pair of sides by distance, matching angles by slope or by copying with compass).
  • Equilateral equiangular, rotate, prove SAS (two sides by distance, included angle by slope or construction).

There is an independent option and a partner option. The course says each student must do at least one collaborative assignment in each segment. If this is that one, use Option 2. If you already did a partner assignment this segment, Option 1 is enough.

What has to be in the file

Graph of the original and the image (graph paper or graphing tech). Both sets of three ordered pairs, labeled, and which scenario you picked.

Shown work: distance formula for every side pair the shortcut needs. Angle work if your scenario is ASA or SAS.

Three sentences that match that scenario: name the exact rule (translation vector, reflection line, or degrees and direction), name two theorems from this module that your triangle actually uses (Triangle Sum, Isosceles, Midsegment, and so on) with numbers from your drawing, and say it is rigid motion because size and shape stayed.

Partner option: you answer those three questions about your partner's triangle, not your own.

Easy miss: picking an obtuse scalene and then only showing two sides, or rotating an equilateral and claiming SSS when the prompt asked for SAS. The shortcut in the title is the one they grade.

Build check before you submit

Obtuse scalene: one angle over 90°, three different side lengths. Count or distance before you transform, so you are not accidentally isosceles.

Isosceles right: one 90°, two legs equal. A clean one is (0, 0), (4, 0), (0, 4). Reflect across an axis so the rule is obvious: (x, y) → (x, −y) or (−x, y).

Equilateral: all sides equal. On a grid this is fussy. Distance every side after you pick points, then rotate around the origin with (y, −x) or (−y, x) so the rule is one of the three from 02.02.

This page does not replace the write-up. Draw it, show the algebra, submit in Canvas.