MathsFreePrintable

Shapes and Properties

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Shapes and Properties

Manaia is planning a geometric exhibition. Solve each challenge using clear mathematical language. For sketches, diagrams do not need to be drawn to scale unless stated.

Classifying shapes

Use properties to identify and compare the shapes on display.

1.A gallery frame is a quadrilateral with exactly one pair of parallel sides. Which name best describes it?

Kite
Trapezium
Rhombus
Rectangle

2.Levi says, “Every square is a rectangle, but not every rectangle is a square.” Is Levi correct? Explain using side and angle properties.

3.Select every true property of an equilateral triangle.

All three sides are equal
All three angles are 60°
It has three lines of symmetry
It has a pair of parallel sides
All its angles are acute

Symmetry in the exhibition

Imagine folding each shape exactly in half. A line of symmetry makes the two halves match.

4.Which shape has no lines of symmetry?

Scalene triangle
Square
Regular pentagon
Rectangle

5.Complete the symmetry record: a rectangle that is not a square has lines of symmetry; a regular hexagon has lines of symmetry.

6.A display tile has four equal sides and two pairs of parallel opposite sides. What is its most specific name if it does not have four right angles?

Design and justify

Use the properties of sides, angles and parallel lines to solve the final gallery challenges.

7.A quadrilateral has two pairs of adjacent equal sides, with the sides in one pair a different length from the sides in the other pair. Name the shape and state one additional property of a typical kite.

8.Hemi labels a shape “parallelogram”. It has opposite sides equal and parallel, and opposite angles equal. Write two more properties that would help confirm the label.

9.The gallery needs a four-sided tile with exactly one pair of parallel sides. Sketch one, mark the parallel sides with matching arrows, and explain why it is not a parallelogram.

10.A regular polygon in the exhibition has 8 sides. What is its name, and how many lines of symmetry does it have?

11.A rectangle has side lengths 9 cm and 4 cm. Calculate its perimeter and area. Include units.

12.A shape has four sides, two pairs of parallel sides and four lines of symmetry. Identify the shape and explain which property rules out an ordinary non-square rectangle.