Mapping Triangle ABC to DEF

Pre-Algebra · Axiom Academy

EXAMPLE Mapping Triangle ABC to DEF Find a sequence of rigid transformations that maps one congruent triangle exactly onto another. Triangle ABC has vertices A(70,210) , B(140,70) , C(210,210) . Triangle DEF has vertices D(210,70) , E(140,210) , F(70,70) , with corresponding vertices , , . Describe a sequence of transformations that maps exactly onto . The image of (dashed) lands exactly on . Nice work! You mapped one triangle onto another using only rigid transformations. Here is what carried the solution: Check congruence first: matching side lengths mean a rigid sequence exists — no stretching or shrinking. Watch orientation: same winding direction means rotations and translations alone suffice; a mirror image would need a reflection. Anchor a vertex: translating B onto E first gives a fixed pivot to rotate around. Order can be folded: the translate-then-rotate sequence is the same map as one rotation about the center (140,140) . Multiple sequences work: any sequence that sends , , is a valid answer. Rigid transformations preserve length, angle, and shape — only position and orientation change. The same reasoning powers congruence proofs, coordinate geometry, and computer graphics.

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