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  • GETSenPhaseMaths display tagshide tags

    This module is included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: Siyavula

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Polygons

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Space and Shape

EDUCATOR SECTION

Memorandum

15.2

(a) concave

(b) concave

(c) convex

16.1

(a) rhombus

(b) trapezium

(c) octagon

(d) quadrilateral polygon

(e) hexagon

(f) heptagon

(g) pentagon

(h) parallelogram

16.2

Figure 1
Figure 1 (graphics1.png)

16.3 108°

17.1 SIMILARITIES

* 4 equally long sides

sides ⁄ ⁄

* diagonals half each other

* 4 corners

DIFFERENCES

* angles of

rhombus not 90°

17.2 SIMILARITIES

* have 2 pairs of equally long sides

* 2 opposite sides are equally long

* have 4 corners

* diagonals halve (bisect) each other

DIFFERENCES

* angles of parallelogram not 90°

18.

(a) kite

(b) trapezium

20.2 ceilings; gates; trusses; bridges; scaffolding

Leaner Section

Content

ACTIVITY: Polygons [LO 3.1, LO 2.3]

15. POLYGONS

15.1 Did you know?

Geometric forms in a plane that are made up of straight lines are called polygons. These are made up of sides, angles or corners and vertices.

Figure 2
Figure 2 (graphics2.png)

15.2 Did you also know?

A polygon is convex if all the lines that join any two vertices are inside the polygon.

All the inner angles are either acute or obtuse angles.

The polygon will be concave if any lines that join two vertices fall outside the polygon.

Then one or more of the inside angles will be a reflex angle.

Figure 3
Figure 3 (graphics3.png)
Figure 4
Figure 4 (graphics4.png)

15.2.1 Are the following polygons convex or concave?

Figure 5
Figure 5 (graphics5.png)
a)

_________________________________

b)

Figure 6
Figure 6 (graphics6.png)

_________________________________

c)

Figure 7
Figure 7 (graphics7.png)

_________________________________

15.3 Also Remember!

The sides of a regular polygon are equally long and all the angles are equally big.

The more sides a regular polygon has, the bigger the inside angles become.

The sides of an irregular polygon are all of different lengths.

Figure 8
Figure 8 (graphics8.png)
Figure 9
Figure 9 (graphics9.png)

15.4 TAKE NOTE!

We can calculate the size of the angles of a regular polygon with the help of this formula:

Figure 10
Figure 10 (graphics10.png)

e.g. Hexagon:

Figure 11
Figure 11 (graphics11.png)

16.1 Work with a friend. Can you say what each of the following polygons are called? Write the name in each figure.

a)

Figure 12
Figure 12 (graphics12.png)

b)

Figure 13
Figure 13 (graphics13.png)

c)

Figure 14
Figure 14 (graphics14.png)

d)

Figure 15
Figure 15 (graphics15.png)

e)

Figure 16
Figure 16 (graphics16.png)

f)

Figure 17
Figure 17 (graphics17.png)

g)

Figure 18
Figure 18 (graphics18.png)

h)

Figure 19
Figure 19 (graphics19.png)

16.2 Calculate the size of each angle of the octagon.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

16.3 What is the size of each angle of a pentagon?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

17.1 Work in groups of three. Cut strips of thick cardboard or use ice cream sticks. Make holes at the ends and join the sticks with split pins. Build a square.

Press on one corner and change it into a rhombus.

Figure 20
Figure 20 (graphics20.png)

Figure 21
Figure 21 (graphics21.png)

  • Now compare the square with the rhombus and see if you can complete the following table:

SIMILARITIES

between rhombus and square

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

DIFFERENCES

between rhombus and square

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

17.2 From other groups of three. Follow the same instructions as for 17.1 but build a rectangle instead. If you press on a corner it will change into a parallelogram.

  • Now complete the table by comparing the rectangle with the parallelogram:

SIMILARITIES

between rectangle and parallelogram

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

DIFFERENCES

between rectangle and parallelogram

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

18. What do we call this geometric figure?

Figure 22
Figure 22 (graphics22.png)
a)

__________________________________________

b)

Figure 23
Figure 23 (graphics23.png)

__________________________________________

19. Form groups of four. Your teacher will say who must do a, b, c, and d.

19.1 Discuss the similarities and differences between:

a) a rhombus and a kite;

b) a trapezium and a parallelogram;

c) a rectangle and a trapezium;

d) a kite and a trapezium.

19.2 Make a poster to explain the above and report back to the class.

20. Did you know?

In maths we say a figure / structure is rigid if it can keep its original form even though pressure is applied to one of its corners, e.g.

Figure 24
Figure 24 (graphics24.png)

Not sturdy

Figure 25
Figure 25 (graphics25.png)

Sturdy

20.1 Divide into pairs. Use cool drink straws and build any rigid structure. See if you can build the highest structure in the class!

20.2 TAKE NOTE!

A triangle is the only polygon that is rigid. It doesn’t change its form when pressure is applied to any of its corners.

Where, do you think, do engineers and builders regularly use triangles to ensure stability in their constructions?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

21. Time for self-assessment

Table 1
  • Tick the applicable block..
 Uncertain Certain
I can explain what the following are:    
  • a polygon
 ___ ___
  • a convex polygon
 ___ ___
  • a concave polygon
 ___ ___
  • a regular polygon
 ___ ___
  • an irregular polygon
 ___ ___
I know the formula to determine / calculate the size of the angles of a regular polygon ___ ___
I can point out the similarities between different geometric forms. ___ ___
I can point out the differences between different geometric forms. ___ ___
I can build a rigid construction with cool drink straws ___ ___

Assessment

Learning Outcome 3: The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment Standard 3.1: We know this when the learner recognises, visualises and names geometric figures and solids in natural and cultural forms and geometric settings, including those previously dealt with.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways.

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