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Parallel and Perpendicular Sides is a free printable Grade 4 math worksheet on sorting shapes by whether they have perpendicular sides, only parallel sides, or neither, aligned to Common Core standard 4.G.A.2. It prints 5 questions with an answer key on its own sheet of paper, in 25 versions that each ask different questions, so no two students in the class work from the same page. Print it from the browser or download it as a PDF — no account, no email.

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All 25 sets ask different questions.

Parallel and Perpendicular Sides

4.G.A.2

NameDate

Sort each one into the right box.

1.Sort each one into the right box.

Sort: a trapezoid with no square corners, regular hexagon, equilateral triangle, square

Has perpendicular sidesParallel sides, none perpendicularNeither
2.Sort each one into the right box.

Sort: a rhombus that is not a square, a parallelogram with no square corners, rectangle, regular hexagon

Has perpendicular sidesParallel sides, none perpendicularNeither
3.Sort each one into the right box.

Sort: a triangle with no square corner, square, regular hexagon, a trapezoid with two square corners

Has perpendicular sidesParallel sides, none perpendicularNeither
4.Sort each one into the right box.

Sort: a parallelogram with no square corners, a trapezoid with no square corners, a rhombus that is not a square, regular pentagon

Has perpendicular sidesParallel sides, none perpendicularNeither
5.Sort each one into the right box.

Sort: a parallelogram with no square corners, regular pentagon, rectangle, right triangle

Has perpendicular sidesParallel sides, none perpendicularNeither

LessonPrint · 4.G.A.2 · Set 1 · free to copy for classroom use

Answer key — Parallel and Perpendicular Sides

Set 1. Prints on its own sheet.

  1. 1.Has perpendicular sides: square; Parallel sides, none perpendicular: a trapezoid with no square corners, regular hexagon; Neither: equilateral triangle
  2. 2.Has perpendicular sides: rectangle; Parallel sides, none perpendicular: a rhombus that is not a square, a parallelogram with no square corners, regular hexagon; Neither: —
  3. 3.Has perpendicular sides: square, a trapezoid with two square corners; Parallel sides, none perpendicular: regular hexagon; Neither: a triangle with no square corner
  4. 4.Has perpendicular sides: —; Parallel sides, none perpendicular: a parallelogram with no square corners, a trapezoid with no square corners, a rhombus that is not a square; Neither: regular pentagon
  5. 5.Has perpendicular sides: rectangle, right triangle; Parallel sides, none perpendicular: a parallelogram with no square corners; Neither: regular pentagon

Questions about Parallel and Perpendicular Sides

What does the Parallel and Perpendicular Sides worksheet cover?

It practices sorting shapes by whether they have perpendicular sides, only parallel sides, or neither — 5 questions for Grade 4, all on Common Core 4.G.A.2: Sort shapes by their parallel and perpendicular sides and by their angles, and pick out right triangles. The instruction to students is “Sort each one into the right box”, and the answer key follows on the next sheet.

Which Common Core standard does Parallel and Perpendicular Sides practice?

CCSS.MATH.CONTENT.4.G.A.2 — 4.G.A.2, under Geometry for Grade 4. The published standard reads: “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.” The worksheet assesses that standard rather than a paraphrase of it.

What age or grade is this worksheet for?

Parallel and Perpendicular Sides is written for Grade 4, typically ages 9-10. It is one of the sheets on 4.G.A.2, so it suits any student working at that standard — including older students revisiting it and younger ones working ahead.

Does Parallel and Perpendicular Sides come with an answer key?

Yes. All 5 answers are generated from the same problems as the questions, so the key cannot drift out of step with the sheet. It starts on a fresh sheet of paper, after the questions, so it is not handed out with the class by accident.

How many different versions of Parallel and Perpendicular Sides can I print?

25 — one per student, and all 25 ask different questions. Set 1 downloads the whole class as a single PDF. Every version is fixed to its own address, so a sheet printed today holds the same problems when you reopen it next week.

Is Parallel and Perpendicular Sides free to print and photocopy?

Yes. Parallel and Perpendicular Sides, its answer key and its 25 versions are free to print and photocopy for your own class, with no account, no email capture and no subscription at the download step. Please do not resell them or republish them as your own.

More practice for 4.G.A.2

Sort shapes by their parallel and perpendicular sides and by their angles, and pick out right triangles.

All Grade 4 worksheets

Last reviewed 2026-09-05. Aligned to 4.G.A.2 of the Common Core State Standards for Mathematics.