Congruence Through Transformations
Aligned to 8.G.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Two figures are congruent if one can be mapped onto the other using only rotations, reflections, and translations. Because these motions preserve size and shape, congruent figures have equal corresponding sides and angles.
Worked example
Triangle ABC has vertices A(0, 0), B(2, 0), C(0, 3). Translating it right 4 gives A'(4, 0), B'(6, 0), C'(4, 3). Every side length matches the original, so the two triangles are congruent.
Practice questions
- Name one type of transformation that always maps a figure onto a congruent copy.
- Triangle DEF is reflected, then translated, onto triangle GHI. Are they congruent? Explain.
- Figure P has a side of 5 cm; its image Q after a rotation — what is the matching side length?
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 por Transformaciones
Dos figuras son congruentes si una puede mapearse sobre la otra usando solo rotaciones, reflexiones y traslaciones. Como estos movimientos conservan tamaño y forma, las figuras congruentes tienen lados y ángulos correspondientes iguales.
Ejemplo: El triángulo ABC tiene vértices A(0, 0), B(2, 0), C(0, 3). Trasladándolo 4 a la derecha se obtiene A'(4, 0), B'(6, 0), C'(4, 3). Cada longitud de lado coincide con el original, así que los dos triángulos son congruentes.
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