Congruence Through Rigid Motions
Aligned to G-CO.B.6 — Common Core State Standards for Mathematics.
What this lesson teaches
Two figures are congruent exactly when some sequence of rigid motions maps one onto the other. Because rigid motions preserve distance and angle, congruent figures have equal corresponding sides and angles. To decide congruence, look for a mapping.
Worked example
Segment AB has A(0,0), B(3,0). Segment CD has C(1,2), D(1,5). Is AB congruent to CD? Length AB = 3, length CD = |5 - 2| = 3. A rotation of 90° plus a translation carries AB onto CD, so they are congruent. The equal lengths confirm a rigid motion exists.
Practice questions
- Triangle 1 has sides 5, 6, 7. Triangle 2 has sides 5, 6, 7. Can a rigid motion map one onto the other?
- A figure is reflected and then translated. Is the image congruent to the original? Explain using preserved quantities.
- Two rectangles both measure 4 by 9 but sit in different places and orientations. Are they congruent? Justify.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Congruencia mediante movimientos rígidos
Dos figuras son congruentes exactamente cuando alguna secuencia de movimientos rígidos mapea una sobre la otra. Como los movimientos rígidos conservan la distancia y el ángulo, las figuras congruentes tienen lados y ángulos correspondientes iguales. Para decidir la congruencia, busca un mapeo.
Ejemplo: El segmento AB tiene A(0,0), B(3,0). El segmento CD tiene C(1,2), D(1,5). ¿Es AB congruente con CD? Longitud AB = 3, longitud CD = |5 - 2| = 3. Una rotación de 90° más una traslación lleva AB sobre CD, así que son congruentes. Las longitudes iguales confirman que existe un movimiento rígido.
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