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GCSE/Mathematics/CCEA

G1Properties of 2D shapes: angles, polygons, triangles, quadrilaterals

Notes

Properties of 2D shapes

Triangles

Sum of interior angles = 180°.

TypeProperty
EquilateralAll sides equal, all angles 60°
IsoscelesTwo equal sides, two equal base angles
ScaleneAll sides and angles different
Right-angledOne angle is 90°

Exterior angle of a triangle = sum of the two opposite interior angles.

Quadrilaterals

Sum of interior angles = 360°.

ShapeSidesAnglesDiagonals
Square4 equal4 right anglesEqual, perpendicular, bisect
RectangleOpposite equal4 right anglesEqual, bisect
ParallelogramOpposite equal & parallelOpposite equalBisect each other
RhombusAll equalOpposite equalPerpendicular bisectors
KiteTwo pairs adjacent equalOne pair opposite equalPerpendicular
TrapeziumOne pair parallel

Polygons (n sides)

  • Sum of interior angles = (n − 2) × 180°.
  • Each interior angle of a regular polygon = (n − 2) × 180° / n.
  • Each exterior angle of a regular polygon = 360° / n.
  • Interior + exterior angle at each vertex = 180°.

Example: regular hexagon (n = 6). Exterior angle = 60°, interior angle = 120°.

CCEA reasoning marks

When a question says "give a reason", quote the geometric fact in standard wording: "angles in a triangle sum to 180°", "exterior angle of a regular pentagon = 360°/5", "opposite angles of a parallelogram are equal". A correct numerical answer without justification loses the B1 reasoning mark on Higher tier.

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Practice questions

Try each before peeking at the worked solution.

  1. Question 14 marks

    Interior angle of a regular polygon

    CCEA Foundation Paper M2 (calculator)

    A regular polygon has 12 sides.

    (a) Calculate the size of each exterior angle. (1 mark)
    (b) Hence write down the size of each interior angle. (1 mark)
    (c) Find the sum of the interior angles of the polygon. (2 marks)

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  2. Question 23 marks

    Find an angle in an isosceles triangle

    CCEA Foundation Paper M1 (non-calculator)

    Triangle ABC is isosceles with AB = AC. The angle at A is 64°.

    (a) Find the size of angle ABC. (2 marks)
    (b) Give a reason for your answer. (1 mark)

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  3. Question 33 marks

    Number of sides from interior angle

    CCEA Higher Paper M6 (calculator)

    The interior angle of a regular polygon is 162°. How many sides does it have?

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Flashcards

G1 — Properties of 2D shapes: angles, polygons, triangles, quadrilaterals

7-card SR deck for CCEA GCSE Mathematics — Leaves topic G1

7 cards · spaced repetition (SM-2)