Similarity Through Dilations
Aligned to 8.G.A.4 — Common Core State Standards for Mathematics.
What this lesson teaches
Two figures are similar if one can be obtained from the other by a sequence of transformations that includes a dilation. Similar figures have equal corresponding angles and proportional corresponding sides.
Worked example
A triangle with sides 3, 4, 5 is dilated by scale factor 2 to sides 6, 8, 10. Each new side is 2 times the original, so the ratio of corresponding sides is 2:1 and the triangles are similar.
Practice questions
- A 2 × 5 rectangle is dilated by a factor of 3. What are its new dimensions?
- Two triangles have all equal angles but different sizes. Are they similar? Explain.
- A figure's sides are 4, 6, 8; a similar figure's shortest side is 6. Find the scale factor and the other sides.
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.
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Semejanza por Dilataciones
Dos figuras son semejantes si una puede obtenerse de la otra mediante una secuencia de transformaciones que incluya una dilatación. Las figuras semejantes tienen ángulos correspondientes iguales y lados correspondientes proporcionales.
Ejemplo: Un triángulo con lados 3, 4, 5 se dilata por un factor de escala 2 a lados 6, 8, 10. Cada lado nuevo es 2 veces el original, así que la razón de lados correspondientes es 2:1 y los triángulos son semejantes.
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