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Features

Tell parallel, perpendicular, and intersecting lines apart
Name lines, sides, and angles with letters and the symbols ∥, ⊥, and ∠
Name triangles by their angles (acute, right, obtuse) and by their sides (equilateral, isosceles, scalene)
Read tick marks, arrows, and right angle squares to name quadrilaterals, and check every name that fits
Fill in the quadrilateral family tree and decide if statements are always, sometimes, or never true
Sort shapes in a Venn diagram by their properties
Every page in color and in black and white
Answer keys included

Skills Covered

Tell parallel, perpendicular, and intersecting lines and segments apart
Name lines, sides, and angles with letters and the symbols ∥, ⊥, and ∠
Name triangles by their angles and by their sides

Read tick marks, arrows, and right angle squares to name quadrilaterals
See that a shape belongs to every group above it: every square is a rectangle and a rhombus
Sort shapes by two properties in a Venn diagram

How to Use This Pack

Five pages on sorting flat shapes by their sides and angles. Page 1 names pairs of lines and segments as parallel, perpendicular, or intersecting, writes ∥ or ⊥ between named lines in a figure, and names the sides and angles of a quadrilateral with letters. Page 2 names seven triangles by their angles (acute, right, obtuse) and by their sides (equilateral, isosceles, scalene), reading the tick marks and right angle squares, then asks which pairs, such as right and isosceles, a triangle can be. Page 3 explains the marks (tick marks for equal sides, arrows for parallel sides, a square for a right angle), gives the best name for eight quadrilaterals, and checks every name that fits in a table. Page 4 fills in the quadrilateral family tree from quadrilateral to square and decides if statements such as "A rectangle is a square" are always, sometimes, or never true. Page 5 sorts eight quadrilaterals in a Venn diagram (4 right angles, 4 equal sides) and lists the shapes that have a given property.

In the Classroom

Before page 1, have students hold two pencils parallel, then perpendicular, then crossing at a slant. Before page 3, draw a rectangle and a square on the board and mark them together: each pair of equal sides gets its own number of ticks, each pair of parallel sides its own number of arrows. On page 4, ask why a square sits under both the rectangle and the rhombus: it has everything each of them has.

At Home

Go on a shape hunt: windows, books, tiles, and street signs. For each one, ask your child to point out a pair of parallel sides and a right angle, and to give its best name. Then ask for another name that also fits, such as a door that is a rectangle and also a parallelogram.

Tips for Success

Parallel lines never meet; perpendicular lines meet at a right angle
Sides with the same number of tick marks are equal; sides with the same arrows are parallel
A small square in a corner shows a right angle
Name a triangle twice: once by its angles and once by its sides
A shape has every feature of the groups above it, so every square is also a rectangle, a rhombus, and a parallelogram

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

4.G.A.1 Draw and find points, lines, line segments, rays, right, acute and obtuse angles, and parallel and perpendicular lines, including in flat shapes.
4.G.A.2 Sort flat shapes by whether they have parallel or perpendicular lines or angles of a certain size, and recognize right triangles as a group.
5.G.B.3 Know that a shape in a smaller group has every feature of the larger group: squares are rhombuses, so all squares have four equal sides.
5.G.B.4 Sort flat shapes into a hierarchy by their properties, such as polygons, quadrilaterals, parallelograms, rectangles and squares.

Classifying Triangles and Quadrilaterals

4th – 5th Grade

Sorting triangles and quadrilaterals by sides and angles. Students name lines and angles with ∥, ⊥ and ∠, classify triangles by angles and sides, name quadrilaterals from their marks and sort shapes in a Venn diagram.

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What’s Included

5 worksheets in color and in black and white, with answer keys (15 pages)
Parallel, perpendicular, and intersecting lines, named with letters and the symbols ∥, ⊥, and ∠
Triangles by angles and by sides, and quadrilaterals named from their tick marks, arrows, and right angles
The quadrilateral family tree, always, sometimes, or never true, and a Venn diagram sort

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Free to print and share

This worksheet is free to download, print, copy, and hand out in your classroom or at home. You do not need to create an account, and there are no watermarks on the PDF.