Classifying Triangles and Quadrilaterals Sort

4th Grade MathGeometry4 pages

About this worksheet

A shape sort for 4th grade against Common Core 4.G.1 and 4.G.2. A bank of eight lettered shapes feeds three tasks: four triangles (scalene right, equilateral, obtuse and isosceles right) and four quadrilaterals (rectangle, trapezoid, rhombus and square), all drawn with right-angle markers where they apply. Triangles split into right versus not right. Quadrilaterals sort three ways by parallel pairs and right angles, which separates the rhombus from the square. Final questions ask which shapes hold perpendicular or parallel sides and why Shape D counts as both a quadrilateral and a parallelogram. Answers included.

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$Classifying Triangles and Quadrilaterals Sort: Geometry - page 1$

$Classifying Triangles and Quadrilaterals Sort: Geometry - page 2$

$Classifying Triangles and Quadrilaterals Sort: Geometry - page 3$

$Classifying Triangles and Quadrilaterals Sort: Geometry - page 4$

Curriculum objectives covered

4.G.1

“Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.”

Reading the right-angle markers and parallel sides in the bank, and listing the shapes with perpendicular or parallel sides in Part 3.

4.G.2

“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.”

Both sorts. The right-versus-not-right triangle columns restate the standard's right-triangle category, and the quadrilateral columns run on parallel and perpendicular presence.

What's inside this worksheet

Shape Bank

Eight diagrams lettered A to H with the evidence drawn in: a scalene right triangle, an equilateral triangle, an obtuse triangle, a rectangle, a trapezoid, a rhombus, a square and an isosceles right triangle.

Part 1: Triangle Sort

Letters go into two columns: contains one right angle (perpendicular sides) or acute-obtuse with none.

Part 2: Quadrilateral Sort

Three columns split the four quadrilaterals: exactly one pair of parallel sides, two pairs with right angles, and two pairs with no right angles. The rhombus lands alone in that last column.

Part 3: Line & Angle Property Check

Which shapes have at least one pair of perpendicular sides, which have parallel sides, and a written explanation of why Shape D fits both the quadrilateral and parallelogram categories.

How teachers use it

Cut and sort first

Copy the bank, cut the eight shapes apart, and let pairs physically sort before writing letters. The rhombus-versus-square argument is the productive one.

Precision language

Ban "diamond" and "slanted square" during Part 2. The column headers give the exact vocabulary to use instead.

Written reasoning

Part 3's Shape D explanation is a two-sentence writing task: four sides makes it a quadrilateral, two pairs of parallel sides make it a parallelogram. Collect and read these.

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