![Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin
1 | P a g e
Form 3 - Chapter 2 – Polygons II [Notes Completely]
Review Form 1 - Chapter 10 - Polygons
10.1 Polygons
Regular Polygons
10.2 Symmetry
To determine and drawing the line(s) of
symmetry of shape
1. A shapehas symmetry if one half of the shape can fit
exactly over the otherhalf.
2. A shapecan have one or more linens of symmetry.
10.3 Triangles
Geometric properties and name of triangles
1. A triangle is a three-sided polygon.
2. A triangle is classified based on:
a) The length of its sides (Figure 7)
b) The sizeof its angles (Figure 8&9)
10.4 Quadrilaterals
To determine and drawing the line(s) of symmetry of quadrilateral
1. A quadrilateral is a polygon with 4 straight sides and4 vertices.
2. Example of quadrilateral and their symmetry. Table1
Quadrilaterals Symmetryof quadrilaterals (diagram) Number of line(s) of symmetry
Square 4
Rectangle 2
Parallelogram 0
Rhombus 2
Trapezium 1](https://image.slidesharecdn.com/mathematics-form3-chapter2polygonsii-191107120424/85/Mathematics-Form-1-Chapter-9-polygons-KBSM-of-form-3-chp-2-1-320.jpg)
Mathematics Form 1-Chapter 9 polygons KBSM of form 3 chp 2
- 1. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 1 | P a g e Form 3 - Chapter 2 – Polygons II [Notes Completely] Review Form 1 - Chapter 10 - Polygons 10.1 Polygons Regular Polygons 10.2 Symmetry To determine and drawing the line(s) of symmetry of shape 1. A shapehas symmetry if one half of the shape can fit exactly over the otherhalf. 2. A shapecan have one or more linens of symmetry. 10.3 Triangles Geometric properties and name of triangles 1. A triangle is a three-sided polygon. 2. A triangle is classified based on: a) The length of its sides (Figure 7) b) The sizeof its angles (Figure 8&9) 10.4 Quadrilaterals To determine and drawing the line(s) of symmetry of quadrilateral 1. A quadrilateral is a polygon with 4 straight sides and4 vertices. 2. Example of quadrilateral and their symmetry. Table1 Quadrilaterals Symmetryof quadrilaterals (diagram) Number of line(s) of symmetry Square 4 Rectangle 2 Parallelogram 0 Rhombus 2 Trapezium 1
- 2. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 2 | P a g e Trapezium 0 Kite 1 Geometric properties and name of quadrilateral Example of quadrilateral and their properties. Table 2 Quadrilaterals Properties Square Rectangle Parallelogram Rhombus Trapezium Kite Form 3 - Chapter 2 – Polygons II 2.1 RegularPolygon 1- A regular polygon has all sides of equal length andall interior angles of equalsize. 2- The number of ________________ of aregular polygon is the same as its _________. Name of Polygons Diagram of Polygons Number of Sides Angles Vertices Symmetries Diagonals Triangle 3 3 Quadrilateral 4 4 Pentagon 5 5 Hexagon 6 6 Heptagon 7 7 Octagon 8 8 Nonagon 9 9 Decagon 10 10 Table 3
- 3. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 3 | P a g e Polygons - A polygon is a plane shape with straight sides. - Polygons are 2-dimensional shapes. - They are made of straight lines, has no curve and the shape is closed (all the lines connect up). Polygon (straight sides) Not a Polygon (has a curve) Not a Polygon (open, not closed) Types of Polygons Regularor Irregular A regular polygon has all angles equal andall sides equal, otherwise it is irregular Regular Irregular Concave or Convex A convex polygon has no angles pointing inwards, no internal angle can be more than 180°. If any internal angleis greater than 180°then the polygon is concave. Convex Concave Simple orComplex A simple polygon has only one boundary and it doesn't cross over itself. A complex polygon intersects itself. Many rules about polygons don't work when it is complex. Simple Polygon (this one's a Pentagon) Complex Polygon (also a Pentagon) More Examples Irregular Hexagon Concave Octagon Complex Polygon (a "star polygon", in this case a pentagram) 2.2 Exterior and InteriorAngles of Polygons
- 4. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 4 | P a g e 180o - (interior angle) = (external angle) (number of thetriangle)X 180o Answer Space: or 180o - (interior angle) = (external angle) Answer Space: or 180o - (exterior angle) = (internal angle) or 180o - (exterior angle) = (internal angle) 1- Exterior angle is ___________________________________________________. 2- Interior angle is ____________________________________________________. 3- External angle and interior angle at a vertex are supplementary that is 180o. 4- The formula of finding external angle, interior angle and its number sides. Sum of external angle 360o Each of external angle 360o n Number sides of regular polygon (From external angle) 360o (external angle) Sum of interior angle = (n - 2) X 180o Each of interior angle (n - 2) X 180o n Number sides of regular polygon (From interior angle) 360o 5- The completely notes of external angle, interior angle and its number sides. Name of Polygons Number of sides Sum of external angle Each of external angle Each of interior angle Sum of interior angle Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 6- Example 1: What is the exterior angle ofa regular octagon? (n - 2) X 180o n 7- Example 2: A polygon has a n sides. Given one of its interior angles is 126o while otherinteriorangles are each equal to 162o. Calculate the numberof sides of the polygon. Interior Angles - An angle inside a shape
- 5. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 5 | P a g e Triangles 90° + 60° + 30° = 180° Now tilt a line by 10°: 80° + 70° + 30° = 180° One angle went up by 10°, other angle went down by 10° The Interior Angles of a Triangle add up to 180° Quadrilaterals (Squares) (A Quadrilateral has 4 straight sides) 90°+ 90°+ 90°+ 90°= 360° Nowtilt a line by 10°: 80°+ 100°+ 90°+ 90°= 360° It still adds up to 360° The Interior Angles of a Quadrilateral add up to 360° Because there are 2 triangles in a square. The interior angles in a triangle addup to 180° and for the square they addup to 360° because the square can be made from two triangles! Pentagon A pentagon has 5 sides, can be made from three triangles, so its interior angle is 3 × 180° = 540° and when it is regular (all angles the same), then each interior angle is 540° / 5 = 108°. The Interior Angles of a Pentagon add up to 540° Exercise 1: The diagram shows a pentagon. What is the size of the angle x°? A 115° B 200° C 235° D 245°
- 6. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 6 | P a g e Exterior Angles – An angle between any side of a shape – A line extended from the next side. - The Exterior Angles of a Polygon add up to 360° When we add up the InteriorAngle and Exterior Angle we get a straight line 180°. They are Supplementary Angles. Exercise 2: The exterior angles of a heptagon are y°, 2y°, 3y°, 3y°, 4y°, 5y° and 6y° What is the value of y? A y = 10 C y = 12.86 B y = 12 D y = 15 Exercise 3: The exterior angles of an octagon are x°, 2x°, 3x°, 4x°, 5x°, 6x°, 7x°, and 8x° What is the sizeof the smallest interiorangle of this octagon? A 10° C 80° B 45° D 100° External Knowledge: - (for polygons) Sides Names Each Interior Angle Each External Angle 1 Monogon Henagon - - 2 Digon - - 3 Trigon Triangle 60° 4 Tetragon Quadrilateral 90° 5 Pentagon 108° 6 Hexagon 120° 7 Heptagon Septagon 128.571° 8 Octagon 135° 9 Nonagon Enneagon 140° 10 Decagon 144° 11 Hendecagon Undecagon 147.273° 12 Decagon Dodecagon 150° 13 Trisdecagon Tridecagon 152.308° 14 Tetradecagon 154.286° 15 Pentadecagon Pentedecagon 156° 16 Hexadecagon Hexdecagon 157.5° 17 Heptadecagon 158.824° 18 Octadecagon 160° 19 Enneadecagon 161.053° 20 Icosagon 162° External Knowledge: - (for complex polygons/star polygons -gram) Regular pentagram Regular hexagram Internal angle (degrees) 36° Internal angle (degrees) 60° External angle (degrees) ___° External angle (degrees) ___ °
- 7. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 7 | P a g e Activity 1:
- 8. Mathematics Form 3 – Chapter 2 Notes Prepared by Kelvin 8 | P a g e Activity 2: