CurriculumGrade 8Mathematics

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

  1. A 2 × 5 rectangle is dilated by a factor of 3. What are its new dimensions?
  2. Two triangles have all equal angles but different sizes. Are they similar? Explain.
  3. A figure's sides are 4, 6, 8; a similar figure's shortest side is 6. Find the scale factor and the other sides.

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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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En español

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.

More Geometry lessons

The Pythagorean Theorem8.G.B.7Properties of Transformations8.G.A.1Congruence Through Transformations8.G.A.2Transformations on the Coordinate Plane8.G.A.3Angle Relationships8.G.A.5The Pythagorean Theorem8.G.B.6

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