Key Concepts:
Angle: A measure of rotation between two lines that meet at a point.
Polygon: A closed 2D shape made from straight lines only (sides do NOT have to be equal length). The lines must not cross each other.
Regular Polygon: A special polygon where ALL sides are equal length AND ALL angles are equal.
Quadrilateral: Any polygon with exactly 4 sides.
Section A: Drawing Basic Angles
1 Draw the following angles in the boxes provided [3]
Instructions: Use your protractor to draw each angle accurately. Label each angle clearly.
a) An acute angle
(Any angle less than 90°)
b) An obtuse angle
(Any angle between 90° and 180°)
c) An angle of 56°
(Use your protractor!)
2 Draw these specific angles using your protractor [4]
Section B: Drawing Combinations of Lines and Angles
3 Draw the following combinations of lines and angles [5]
a) Draw three lines that meet at a point, forming two acute angles
Hint: Start with a point, then draw three lines from it. Check that two of the angles formed are acute (less than 90°).
b) Draw four lines that meet at a point, with one right angle and two obtuse angles
Hint: Use your protractor to ensure accuracy.
c) Draw two intersecting lines forming angles of 45° and 135°
Hint: When two straight lines cross, they create two pairs of equal angles.
Section C: Types of Triangles
4 Draw these triangles based on the given descriptions [5]
Tip: Try drawing more than one example of each triangle type in the box to show different variations!
a) An equilateral triangle
All sides equal, all angles 60°
b) An isosceles triangle
Two sides equal, two angles equal
c) A right-angled triangle
One angle = 90°
d) A scalene triangle
All sides different lengths
e) A right-angled isosceles triangle
One 90° angle, two equal sides
Section D: Understanding and Drawing Polygons
What is a Polygon?
A polygon is a closed 2D shape made entirely from straight lines. The lines must connect to form a complete shape with no gaps. The lines must NOT cross each other. The sides do NOT have to be the same length (unless it's a regular polygon).
5 Which of these are polygons? Write YES or NO [5]
a) A triangle ___________
b) A circle ___________
c) A square ___________
d) A shape with one curved side and three straight sides ___________
e) A pentagon (5-sided shape) ___________
6 Draw these polygons in the boxes [6]
Remember: Polygons are closed shapes made only from straight lines. The sides don't have to be the same length. Use a ruler!
b) A quadrilateral (4 sides)
Section E: Regular Polygons
Regular Polygons:
A regular polygon has ALL sides equal in length AND ALL angles equal in size.
Examples: equilateral triangle, square, regular pentagon, regular hexagon
7 Draw these regular polygons as accurately as you can [4]
a) An equilateral triangle
(All sides equal, all angles 60°)
b) A square
(All sides equal, all angles 90°)
c) A regular pentagon
(5 equal sides, 5 equal angles)
d) A regular hexagon
(6 equal sides, 6 equal angles)
Section F: Special Quadrilaterals
8 Draw a few examples of each special quadrilateral [12]
Use a ruler and pay attention to the specific properties of each shape!
a) Squares
All sides equal, all angles 90°
b) Rectangles (not squares)
Opposite sides equal, all angles 90°
c) Rhombuses
All sides equal, opposite angles equal
d) Parallelograms (not rectangles)
Opposite sides parallel and equal
e) Kites
Two pairs of adjacent equal sides
f) Trapeziums
One pair of parallel sides
Section G: Combining Polygons and Angles
9 Draw shapes with specific angle requirements [6]
a) Draw a quadrilateral with two right angles, one acute angle and one obtuse angle
Hint: Angles in a quadrilateral sum to 360°. Two right angles account for 180°, so the remaining two angles must also sum to 180° — meaning one must be acute and one obtuse. Label all four angles clearly.
b) Draw a pentagon where three angles are 90° and mark them
Hint: Angles in a pentagon sum to 540°. Three right angles account for 270°, leaving 270° shared between the other two angles. Try drawing a staircase-style or L-shaped pentagon. Use the right angle symbol to mark the 90° angles.
c) Draw an octagon with at least four right angles
Hint: An octagon has 8 sides. Try drawing a staircase or cross-like shape — these naturally produce right angles. Your octagon will be non-convex (some corners will point inward).
10 Create composite shapes (combining polygons) [6]
a) Draw a shape made by joining two equilateral triangles together along one side
What is this shape called?
Name: _______________________________________________
b) Draw a hexagon by combining a square and two equilateral triangles
Place one triangle on top of the square and one on the bottom.
c) Draw a pattern using at least 3 regular polygons of your choice
Be creative! The polygons can be the same or different types.
Total: 56 marks
Mark Scheme
1. [3] — 1 mark each for:
(a) Any angle clearly less than 90°, labelled as acute.
(b) Any angle clearly between 90° and 180°, labelled as obtuse.
(c) An angle of 56° ± 2°, drawn with a protractor and labelled.
2. [4] — 1 mark each for angles within ± 2°:
(a) 35° (b) 125° (c) 90° (right angle symbol acceptable) (d) 160°
3. [5]
(a) [2] Three rays from a common point; two of the three gaps between rays are acute (less than 90°). The third gap will be a reflex angle. Award 1 mark for three rays meeting at a point, 1 mark for two visible acute angles.
(b) [2] Four rays from a common point; one gap is 90° (± 2°), and at least two other gaps are obtuse. Award 1 mark for correct structure, 1 mark for correct angle types.
(c) [1] Two straight lines crossing; all four angles labelled as 45°, 135°, 45°, 135° (or angles showing two pairs of equal vertically opposite angles).
4. [5] — 1 mark each for a correctly drawn and labelled example:
(a) Equilateral triangle: all three sides equal length, all angles 60°.
(b) Isosceles triangle: exactly two sides equal, base angles equal.
(c) Right-angled triangle: one angle of 90° (right angle symbol required).
(d) Scalene triangle: all three sides visibly different lengths.
(e) Right-angled isosceles triangle: one 90° angle and two 45° angles; two equal sides.
5. [5] — 1 mark each:
(a) YES (b) NO (circle has a curved side) (c) YES (d) NO (has a curved side) (e) YES
6. [6] — 1 mark each for a closed shape with straight lines only and the correct number of sides:
(a) 3 sides (b) 4 sides (c) 5 sides (d) 6 sides (e) 7 sides (f) 8 sides.
Sides do not need to be equal. Shape must be closed with no crossing lines.
7. [4] — 1 mark each. Shapes must look regular (all sides and angles visibly equal):
(a) Equilateral triangle (b) Square (c) Regular pentagon (d) Regular hexagon.
8. [12] — 2 marks each (1 for a valid drawing, 1 for showing the defining properties clearly):
(a) Square: all four sides equal, all angles 90°.
(b) Rectangle: two pairs of equal sides, all angles 90°; must not be a square.
(c) Rhombus: all four sides equal, opposite angles equal; must not look like a square.
(d) Parallelogram: two pairs of parallel sides; must not look like a rectangle.
(e) Kite: two pairs of adjacent equal sides; one axis of symmetry.
(f) Trapezium: exactly one pair of parallel sides.
9. [6] — 2 marks each:
(a) Quadrilateral with two right angles (marked), one acute angle and one obtuse angle, all four labelled. Angles must visibly sum to 360°. [1 mark for valid quadrilateral with two right angles; 1 mark for correct acute/obtuse pair.]
(b) Pentagon with three right angles marked; the other two angles must each be greater than 90° (they sum to 270°, so each is 135° if equal). [1 mark for pentagon with three right angles; 1 mark for remaining angles plausibly summing to 270°.]
(c) Octagon with at least four right angles, forming a non-convex (staircase-style) shape. [1 mark for an 8-sided closed shape; 1 mark for at least four visible right angles.]
10. [6] — 2 marks each:
(a) Two equilateral triangles joined along one side forming a rhombus (accept "diamond"). [1 mark for correct shape; 1 mark for correct name.]
(b) A square with one equilateral triangle on top and one on the bottom, forming a 6-sided shape (hexagon). Triangles must share a full side with the square. [1 mark for hexagon shape; 1 mark for correct construction.]
(c) A creative pattern using at least 3 regular polygons. [1 mark for using 3 or more regular polygons; 1 mark for a coherent, connected pattern.]