Classifying shapes by line properties
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category
Lesson
Set out your lesson
Classify by side relationships and right-angle properties, allowing overlapping categories and rotated figures.
Before teaching
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Ask the learner to draw a pair of parallel lines and a pair of perpendicular lines. Have them indicate a right angle. If they use “looks straight” instead of side relationships, rehearse those ideas before sorting.
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Classify by side relationships and right-angle properties, allowing overlapping categories and rotated figures.
Classify by side relationships and right-angle properties, allowing overlapping categories and rotated figures.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Defining Attributes of Rectangles and Parallelograms
Before you open · source notes
Rectangle and parallelogram attributes support classifying shapes by line properties. Not every circle theorem.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk how a rectangle and a parallelogram are alike and different using sides or angles.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Defining Attributes of Rectangles and Parallelograms.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Sort a set of quadrilaterals into those with parallel sides and those without
- Identify which triangles in a set are right triangles
- Classify shapes that have both perpendicular and parallel sides
“If you show your child a mixed set of triangles and quadrilaterals, can they sort them into groups — like "shapes with at least one right angle" or "shapes with parallel sides" — and explain their reasoning?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 9–11
Standards