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Shapes and Properties Worksheet

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Shapes and Properties Worksheet

Arjun, Mei and Finn are helping plan a football tournament. Use shape properties, angle facts and symmetry to check their designs. Give reasons where asked; diagrams are not necessarily drawn to scale.

Shape clues

Identify each shape from its properties.

1.The tournament badge is a quadrilateral with two pairs of adjacent equal sides, but not all four sides are equal. What type of quadrilateral could it be?

2.A corner flag has a quadrilateral shape with exactly one pair of parallel sides. In New Zealand, what is this shape commonly called?

Parallelogram
Trapezium
Kite
Rhombus

3.A team logo is a parallelogram with one angle measuring 68°. What is the size of the adjacent angle? Explain the angle property you used.

Angle investigation

Use triangle and quadrilateral angle properties to solve the tournament design problems.

4.Mei designs a triangular pennant with angles of 47° and 63°. Find the third angle.

5.A four-sided banner has interior angles 90°, 85°, 105° and x°. Find x. Show or describe your calculation.

6.True or false? Every rectangle is a parallelogram. Give one property that supports your answer.

TrueFalse

Symmetry and classification

Think carefully about what must be true, rather than what is true for just one example.

7.How many lines of symmetry does a regular hexagon have? Describe how they are arranged.

8.A regular pentagon is printed on the tournament programme. How many lines of symmetry does it have?

9.Finn says, “A parallelogram always has two lines of symmetry because it has two pairs of parallel sides.” Is Finn correct? Explain using a counterexample or a property.

10.A quadrilateral has exactly one pair of parallel sides and two right angles. What can you conclude about its other two angles?

Make and defend a design

Use a ruler and protractor if available. Check that each construction matches its stated properties.

11.Draw an isosceles triangle with a 6 cm base and a 40° angle at each end of the base. Find the third angle, then explain why your drawing has the required properties.

12.Create a quadrilateral badge with exactly one line of symmetry and two pairs of adjacent equal sides. Name the shape and state where its line of symmetry lies.