Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Once students can recognize parallel lines, perpendicular lines and types of angles, they can use those features to sort shapes. A figure might have one pair of parallel sides, two pairs, or none. It might have perpendicular sides or not, and it might contain right, acute or obtuse angles. Classifying by these properties is more powerful than classifying by appearance, because it works even when a shape is rotated or stretched.
Quadrilaterals are a rich example. A trapezoid has at least one pair of parallel sides (under the inclusive definition many curricula use), a parallelogram has two pairs, and a rectangle has two pairs plus four right angles. Triangles can be sorted by their largest angle, and the standard singles out right triangles as a category: any triangle with one right angle, however it is turned. Students build and use Venn diagrams or sorting charts to show which figures share which properties.
A square turned on its corner is often called a diamond and not a square. Measuring its sides and angles shows it still has every property of a square.
Students believe a square cannot also be a rectangle. Sorting by properties shows a square has everything a rectangle needs, so it belongs in both groups.
A right triangle with its right angle at the top is often overlooked. Check each corner with a square corner tool.
Sort a square, a trapezoid with exactly one pair of parallel sides, a right triangle and a regular hexagon by two questions: Does it have perpendicular sides? Does it have parallel sides?
Answer: Both questions yes: square. Parallel only: trapezoid and regular hexagon (its 6 sides form 3 parallel pairs). Perpendicular only: right triangle.
Give small groups a set of shape cards and a two-circle Venn diagram labeled "has parallel sides" and "has a right angle." Debating where a rotated square or a kite belongs builds property-based reasoning.
Tests often ask students to select all shapes that fit a description or to name a property two shapes share. Encourage students to check each property with a tool, such as a ruler for parallel sides or an index card corner for right angles.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) Parallelogram
By definition a parallelogram has two pairs of parallel sides. A trapezoid is only guaranteed one pair.
Answer: B) A triangle with angles 90°, 45°, 45°
A right triangle has exactly one right angle. Only the triangle with a 90° angle qualifies.
Answer: A) Rectangle
The sides of a rectangle meet at right angles, so they are perpendicular. The other shapes have no right angles.
Answer: 2 (also accepted: two)
Each pair of opposite sides is parallel, so a rectangle has 2 pairs.
Answer: C) It is still a square because its sides and angles are unchanged
Turning a shape does not change its side lengths or angles, so it is still a square.
Answer: B) No, every pair of sides in a triangle meets
Every two sides of a triangle meet at a vertex, so no two sides can be parallel.
A full lesson with slides, activities and an exit ticket on classifying shapes by lines and angles, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.G.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn classifying shapes by lines and angles into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Yes. A rectangle is a quadrilateral with four right angles, and a square has four right angles, so every square is also a rectangle.
In fifth grade, 5.G.B.3 and 5.G.B.4 build a hierarchy of shapes, explaining that properties of a category belong to all its subcategories.