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Angles and Shapes Properties

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Angles and Shapes Properties

Help plan a geometric sign for a car wash fundraiser. Use angle and shape properties to solve each challenge. Show working where needed.

Angles and triangles

Use angle facts to work out what each shape can be.

1.A triangular sign has side lengths 5 cm, 5 cm and 8 cm. Classify it by its sides. Explain which side-length clue you used.

2.The three interior angles of a triangle add to 180°. Two angles in a triangular sign are 48° and 67°. Find the third angle and classify the triangle by its angles.

3.A triangular pennant has one 90° angle and two equal sides. What is its third angle? Classify the triangle by its angles and by its sides.

4.A regular hexagon is used as a badge. What is the smallest positive turn that maps it onto itself? Explain how you know.

Shape properties and transformations

Check how shapes are built, moved and compared.

5.Which set lists three properties of an equilateral triangle? Choose one answer.

Three equal sides, three 60° angles and three lines of symmetry
Two equal sides, one 90° angle and one line of symmetry
Three unequal sides, three equal angles and no lines of symmetry
Four equal sides, four right angles and two lines of symmetry

6.Jai moves a logo 4 units right and 3 units up. The logo’s point P starts at (2, 1). What are the coordinates of P after the translation?

7.A point on a logo is at (−3, 2). It is reflected across the y-axis. Give the image coordinates and state which coordinate changes sign.

8.Two similar triangular signs have corresponding side lengths in the ratio 3:5 (small to large). If the smaller sign has a perimeter of 18 cm, find the larger perimeter.

9.Two similar triangles have corresponding sides AB = 6 cm and DE = 9 cm. Side BC corresponds to EF and is 8 cm. Find EF.

10.A smaller triangular logo has an area of 12 cm². A similar larger logo is made with a side-length scale factor of 2:3 (small to large). Find the larger area and explain why the area does not use the same scale factor as the side lengths.

11.Design a quadrilateral for the fundraiser sign that has exactly two lines of symmetry. Draw it and name the shape. Add a sentence explaining how its symmetry lines divide it.