4.G.2: Classify Shapes by Lines and Angles
Also written as 4.G.A.2 and CCSS.MATH.CONTENT.4.G.A.2 · Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
The Official Wording
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.
Common Core State Standards, Grade 4, Geometry · Read it at the source · Checked October 14, 2026
What 4.G.2 Means in Plain English
Fourth graders sort shapes with yes-or-no questions about sides and corners. Does it have a pair of parallel sides? A right angle? A trapezoid says yes to the first, a kite with no square corners says no to both, and a triangle with a square corner is a right triangle.
Third grade sorted shapes by side lengths and square corners (3.G.1). Here the 4.G.1 vocabulary becomes the sorting rules. In 5th grade the groups nest: whatever is true of every rectangle is true of every square (5.G.3), and the groups grow into a family tree (5.G.4).
4.G.2 I Can Statements
- I can sort shapes by whether they have parallel sides.
- I can sort shapes by whether they have right, acute or obtuse angles.
- I can pick out the right triangles in a set of triangles.
4.G.2 Worked Example
Six shape cards sorted into a table that asks two questions: any parallel sides, and any right angles?
Sort six shape cards into a two-by-two table, “Any parallel sides?” across the top and “Any right angles?” down the side: a rectangle, a parallelogram with no square corners, a trapezoid with two right angles, a right triangle, a kite with no square corners, and a triangle with three equal sides. Which cards are right triangles?
- Lay a ruler along each pair of opposite sides and extend them. Sides that would never meet are parallel.Parallel sides: rectangle, parallelogram, trapezoid
- Check every corner of every card with the corner of an index card.Right angle: rectangle, trapezoid, right triangle
- A card goes in the cell where its two answers meet.Both: rectangle, trapezoid. Parallel sides only: parallelogram
- The cards left over fill the other two cells.Right angle only: right triangle. Neither: kite, equal-sided triangle
- Only one triangle has a square corner, and one square corner is all a right triangle needs.Right triangles: 1 card
Check it: Count the cards in the table: 2 + 1 + 1 + 2 = 6, so every card landed in exactly one cell.
Common Mistakes with 4.G.2
Parallel and perpendicular swapped
The two short sides of a right triangle called parallel because both are “straight lines”
Try this: Extend both sides with a ruler. Sides that meet in a square corner are perpendicular, and sides that never meet are parallel.
A right triangle only one way up
A right triangle whose square corner points up not counted, because the square corner “belongs at the bottom”
Try this: Turn the triangle until the square corner sits at the bottom, then turn it back. The angle never changed, so neither did the name.
Checking only one pair of sides
A trapezoid sorted into “no parallel sides” because its two slanted sides are not parallel
Try this: Check every pair of opposite sides, not just the first pair you see. One parallel pair is enough for a yes.
Where 4.G.2 Fits
Practice 4.G.2
Quick Check
- Can a triangle have a pair of parallel sides?
- Which of these has perpendicular sides: a rectangle, a rhombus with no right angles, or a trapezoid with two right angles?
- A triangle has angles of 90°, 50° and 40°. Is it a right triangle?