5th Grade Classifying Two-Dimensional Figures Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Classifying Two-Dimensional Figures – Maths PDF

Each answer explains which properties decide the name of the figure. When a shape belongs to several groups, the answer shows why. Check that your reasons use sides, angles or parallel lines.

Grade 5 · Common Core State Standards: 5.G.B.3, 5.G.B.4

Exercise 1 – Name the figure

It has 4 equal sides and 4 right angles. That makes it a square.

Square

Exercise 2 – Squares and rectangles

A rectangle has 4 right angles and opposite sides equal. Every square has these properties.

True

Exercise 3 – Rectangles and squares

A rectangle that is 6 cm long and 3 cm wide has 4 right angles, but its sides are not all equal, so it is not a square.

False

Exercise 4 – Four equal sides

Two pairs of parallel sides make it a parallelogram. Four equal sides make it a rhombus. With no right angles it is not a square.

Rhombus

Exercise 5 – Properties of parallelograms

Answers can vary. Three correct properties:

It has 4 sides, so it is a quadrilateral.
It has two pairs of parallel sides.
Opposite sides are equal in length.

4 sides, two pairs of parallel sides, opposite sides equal

Exercise 6 – Triangle with three equal sides

All three sides are 5 cm, so the triangle is equilateral.

Equilateral

Exercise 7 – Right triangle sides

The sides 3, 4 and 5 are all different: scalene. There is one right angle: right triangle.

Scalene right triangle.

Scalene right triangle

Exercise 8 – Angles 40, 70, 70

All three angles are less than 90°.

Acute triangle

Exercise 9 – Angles 30, 30, 120

One angle, 120°, is greater than 90°.

Obtuse triangle

Exercise 10 – Sides 6, 6, 9

Two sides are equal and the third is different.

Isosceles

Exercise 11 – Place the shapes

The square has both properties, so it goes in the overlap. The 6 by 3 rectangle has only right angles. The rhombus has only equal sides.

Completed Venn diagram.

Rhombus: left only; square: overlap; rectangle: right only

Exercise 12 – Complete the tree

A parallelogram with 4 right angles is a rectangle.

A tree diagram of the quadrilateral family.

Rectangle

Exercise 13 – Two pairs of parallel sides

A rectangle, a rhombus and a parallelogram each have two pairs of parallel sides. The trapezoid has only one pair.

A, B and D have two pairs.

A, B and D

Exercise 14 – Square or rhombus

A rhombus is a quadrilateral with 4 equal sides. A square has 4 equal sides, so it has the main property of a rhombus. The right angles are extra.

A square has 4 equal sides, so it is a rhombus.

Exercise 15 – Picture frame

Every property fits several groups.

Square (most specific)
Rectangle: 4 right angles
Rhombus: 4 equal sides
Parallelogram: two pairs of parallel sides
Quadrilateral: 4 sides

Square, rectangle, rhombus, parallelogram, quadrilateral

Exercise 16 – Garden bed

The sides are not all equal, since 8 ft and 3 ft are different. It has four right angles, so it is a rectangle.

Not a square; it is a rectangle

Exercise 17 – Road sign

Three equal sides: equilateral. Each angle is less than 90°: acute.

Equilateral and acute

Exercise 18 – Rhombus must be a square

A rhombus has 4 equal sides, and this one has sides of 5 cm. A square needs 4 right angles. This rhombus has angles of 60° and 120°, so it has no right angle.

Priya is wrong: this rhombus is not a square.

Exercise 19 – Cutting a triangle

(a) All sides are different: scalene.

(b) One right angle: right triangle.

(a) Scalene; (b) right; (c) 36 in

Exercise 20 – Quilt patches

(a) Two equal sides: isosceles.

(b) \(5+5+8=18\) inches.

(d) \(28-18=10\).

(a) Isosceles; (b) 18 in; (c) 28 in; (d) the rhombus, by 10 in

All Grade 5 chapters: Grade 5 math.

Voter.. post

Print this page

First page of the PDF: 5th Grade Classifying Two-Dimensional Figures Worksheet Solutions (PDF)

Download PDFDownload the 5th Grade Classifying Two-Dimensional Figures Worksheet Solutions (PDF, 66 KB)