A dilation has scale factor 2.5. A preimage side is 5. Find the image side.
Unit 05 · Lesson 02 · Similarity, Dilations & Proportional Reasoning
Similarity Through Transformations
Use dilations and proportional relationships to compare figures, construct scale models, and measure inaccessible quantities.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to use dilations and proportional relationships to compare figures, construct scale models, and measure inaccessible quantities.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Use dilations and proportional relationships to compare figures, construct scale models, and measure inaccessible quantities.
k=\frac{\text{image length}}{\text{preimage length}}\frac{a}{d}=\frac{b}{e}=\frac{c}{f}AA,\ SAS\sim,\ SSS\sim
Worked reasoning
Process: Establish similarity first, write a proportion with matching sides, solve, and check that the magnitude agrees with the scale factor.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: Corresponding side ratios must be written in a consistent order; mixing image-to-preimage and preimage-to-image reverses the scale factor.
Khaemenes Academy · Open-Age Geometry
Similarity Through Transformations
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Triangles are similar. A side 8 corresponds to 8; a side 9 corresponds to x. Find x.
Which angle evidence alone is sufficient for triangle similarity?
How does a dilation with scale factor 1/2 affect angle measure?
A 1:50 drawing shows a wall 8 cm long. What is the actual length?
Why should scale units be written explicitly?