Edexcel Mathematics (4XMAF) -Unit 1 - 4.2 Polygons- Study Notes- New Syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.2 Polygons- Study Notes- New syllabus
Edexcel Mathematics (4XMAF) -Unit 1 – 4.2 Polygons- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A recognise and give the names of polygons
Notes: parallelogram, rectangle, square, rhombus, trapezium, kite, pentagon, hexagon and octagon
B understand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals
The four angles of a quadrilateral are 90°, (x + 15)°, (x + 25)° and (x + 35)°. Find x.
C understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Names of Polygons
A polygon is a closed 2-D shape made only from straight sides.
Polygons are named according to the number of sides they have.
Common Polygons
3 sides → Triangle
4 sides → Quadrilateral
5 sides → Pentagon
6 sides → Hexagon
8 sides → Octagon
Special Quadrilaterals
Parallelogram
Rectangle
Square
Rhombus
Trapezium
Kite
Key Idea
The name of a polygon tells you how many sides it has.
Example 1:
Name a polygon with 5 sides.
▶️ Answer/Explanation
5 sides correspond to a pentagon.
Conclusion: Pentagon.
Example 2:
Name a polygon with 8 sides.
▶️ Answer/Explanation
8 sides correspond to an octagon.
Conclusion: Octagon.
Example 3:
State the name of a 4-sided polygon.
▶️ Answer/Explanation
A 4-sided polygon is called a quadrilateral.
Conclusion: Quadrilateral.
Quadrilaterals and Angle Sum
A quadrilateral is a polygon with four sides.
Examples include rectangles, squares, parallelograms and trapeziums.
Angle Sum Property
The interior angles of any quadrilateral always add up to:
\( 360^\circ \)
This rule can be used to find unknown angles.
Key Idea
Add all four angles and set the total equal to \( 360^\circ \).
Example 1:
The four angles of a quadrilateral are \( 90^\circ,\; (x+15)^\circ,\; (x+25)^\circ,\; (x+35)^\circ \). Find \( x \).
▶️ Answer/Explanation
\( 90 + (x+15) + (x+25) + (x+35) = 360 \)
\( 3x + 165 = 360 \)
\( 3x = 195 \)
\( x = 65 \)
Conclusion: \( x = 65^\circ \).
Example 2:
Three angles of a quadrilateral are \( 80^\circ,\; 95^\circ,\; 120^\circ \). Find the fourth angle.
▶️ Answer/Explanation
Sum known angles:
\( 80 + 95 + 120 = 295^\circ \)
\( 360 – 295 = 65^\circ \)
Conclusion: \( 65^\circ \).
Example 3:
All angles of a quadrilateral are equal. Find each angle.
▶️ Answer/Explanation
\( 360^\circ ÷ 4 = 90^\circ \)
Conclusion: Each angle is \( 90^\circ \).
Properties of Special Quadrilaterals
Different quadrilaterals have different side and angle properties.
Parallelogram
Opposite sides are equal and parallel
Opposite angles are equal
Adjacent angles add to \( 180^\circ \)
Rectangle
Opposite sides are equal and parallel
All angles are \( 90^\circ \)
Square
All sides equal
All angles \( 90^\circ \)
Opposite sides parallel
Rhombus
All sides equal
Opposite angles equal
Trapezium
One pair of parallel sides
Kite
Two pairs of equal adjacent sides
One pair of opposite angles equal
Key Idea
A square is both a rectangle and a rhombus.
Example 1:
In a parallelogram, one angle is \( 70^\circ \). Find the adjacent angle.
▶️ Answer/Explanation
Adjacent angles add to \( 180^\circ \)
\( 180^\circ – 70^\circ = 110^\circ \)
Conclusion: \( 110^\circ \).
Example 2:
All sides of a quadrilateral are equal and each angle is \( 90^\circ \). Name the shape.
▶️ Answer/Explanation
Equal sides + right angles.
Conclusion: Square.
Example 3:
A quadrilateral has exactly one pair of parallel sides. Name it.
▶️ Answer/Explanation
One pair of parallel sides.
Conclusion: Trapezium.