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

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

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This classify shapes answers for 5th Grade covers classifying two-dimensional figures (Common Core 5.G.B.3, 5.G.B.4), with a free PDF to print.

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

Classify shapes answers: exercises 1 to 10

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

Exercises 11 and up

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

Key facts behind this classify shapes answers

Key facts

A quadrilateral has 4 sides; a parallelogram has two pairs of parallel sides.
A rectangle has 4 right angles; a rhombus has 4 equal sides; a square has both.
Every square is a rectangle and a rhombus, but not every rectangle is a square.
Triangles by sides: equilateral, isosceles, scalene.
Triangles by angles: acute, right, obtuse.

How to use this classify shapes answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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