7.5.A
The Standard
generalize the critical attributes of similarity, including ratios within and between similar shapes
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students match corresponding sides and angles in two figures. They explain that corresponding angles are equal, side lengths share one scale factor, and matching ratios within each figure are equal.
What Mastery Looks Like
- Given measurements or a diagram, students correctly pair corresponding parts and find a consistent scale factor. They use angle relationships and side ratios to justify similarity, not visual appearance alone.
Common Misconceptions
- Students often compare sides that do not correspond or switch the ratio order midway. They may use equal differences instead of equal ratios, or decide figures are similar because they look alike. Some think proportional sides alone guarantee similarity for every polygon and ignore corresponding angles.
How to Assess It
- Exit ticket: Two quadrilaterals have corresponding sides 3, 4, 5, 6 and 6, 8, 10, 12, with equal corresponding angles. Find the scale factor, compare 3/4 with 6/8, and explain why the figures are similar.
Lesson moves
Ways to Teach It
Give pairs of scaled paper polygons; students measure sides and angles, then record matching side ratios and equal angles in a table.
Ask, “Can two quadrilaterals have proportional corresponding sides but not be similar?” Students draw an example and identify the missing condition.
Run a card sort with diagrams, angle measures, and side lengths; students match similar pairs and write the scale factor for each.
Use a floor plan and room measurements; students test whether the drawing is similar to the room and calculate its scale factor.
Keep exploring
Related Standards
- 8.3.B
compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
- K.6.D
identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably
- 1.6.A
classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language
- 8.3.A
generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
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