Unit 11 Summary

Pre-Algebra · Axiom Academy

SUMMARY Unit 11 Summary: Transformations A quick review of how figures slide, flip, turn, and resize — and how those moves define congruence and similarity. Congruence is defined by transformations — if you can map one figure onto another using only rigid transformations, the two figures are congruent. Rigid transformations preserve distances, angles, and area; dilations preserve angles and shape but change size. Each transformation has a coordinate rule that predicts where a point moves, with no graphing required. Recognizing symmetry helps you analyze figures quickly, and shows up across mathematics, science, and art. Many transformation problems have multiple valid solutions — flexibility in approach is part of the skill. Core Concept The Four Transformations Every transformation in this unit is one of four moves: Translation (slide): moves every point the same distance in the same direction — no turning or flipping. Reflection (flip): flips a figure across a line, making a mirror image; each point is equidistant from the line on opposite sides. Rotation (turn): turns a figure around a fixed center by a given angle; every point keeps its distance from the center. Dilation (resize): enlarges or shrinks a figure by a scale factor from a center point — changes size, keeps shape. Core Concept Rigid vs. Non-Rigid The kind of transformation decides whether figures end up congruent or merely similar.

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