Curriculum placement
Grade 8. This describes the skill, not a learner estimate.
Dilations and similarity
Use dilations and rigid motions to establish similarity
Problem types
- Coordinates after a dilation
- Find a dilation's scale factor
- Missing side of similar triangles
- Similarity from a dilation and a rigid motion
- Write the rule of a dilation
- Show the work: angle, scale factor and sides of similar triangles
- How perimeter and area change under a dilation
Builds on
- Translations, reflections, and rotations
- Scale drawings of lengths and areas
- What slides, flips, and turns keep the same · Earlier idea
Slides, flips and turns keep every length, every angle and every pair of parallel lines. A dilation keeps the angles and the parallel lines too, but it multiplies every length by the scale factor.
Leads to
- How a dilation changes a figure
- Proving triangles similar
- Slope of a line · See it applied
Scaling a right triangle's horizontal and vertical changes by the same factor preserves their ratio. This explains why triangles along one straight line give the same slope.
Related skills
- Congruence criteria for triangles · Shared foundations
- Symmetries of a polygon · Shared foundations
- What a transformation keeps · Shared foundations
Open the interactive map to explore lessons and skill connections.