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ACTIVITY 1
To apply understanding of quadrilaterals and their properties in problems
[LO 3.7, 4.4]
1. Calculate the values of a, b, c , etc. from the information given here and in the sketch, and answer the question.
1.1 The diagram shows a square with one side 3 cm. a = an adjacent side.
b = the diagonal. c = the area of the square.
Why does the diagonal make a 45 ° angle with the side?
1.2 A rhombus is given, with long diagonal = 8 cm and short diagonal = 6 cm. a = side length.
b = area of rhombus..
Why are you allowed to use the Theorem of Pythagoras here?
1.3 The diagram shows a rectangle with a short side = 5 cm and a diagonal = 13cm.
a = the long side. b = area of rectangle.
Why is the other diagonal also 13 cm?
1.4 The figure is a parallelogram with one internal angle = 65°, height = 3 cm and long side = 9 cm.
a = smaller of internal angles. b = larger of internal angles. c = area of parallelogram
Explain why this parallelogram has the same area as a 3 cm by 9 cm rectangle.
2. Calculate the value of x from the information in the sketches.
2.1 An equilateral triangle is given, with side 15 cm and area = 45 cm 2 . x = height of triangle.
Why does this triangle have a 60 ° internal angle?
2.2 The diagram shows a trapezium with longest side 23 cm and the side parallel to
it 15 cm and height = 8 cm.
x = area of trapezium.
Why are the two marked internal angles supplementary?
2.3 The figure is a kite with area 162 cm 2 and a short diagonal of 12 cm. x = long diagonal.
Why do the internal angles of the kite add up to 360 ° ?
2.4 The sketch shows the kite from question 2.3 divided into 3 triangles with equal areas (ignore the dotted line). x = top part of long diagonal.
3. These problems require you to make equations from the information in the sketch, using your knowledge of the characteristics of the figure. Solving the equations gives you the value of x .
3.1 The figure is a rhombus with two angles marked 3 x and x respectively.
Why can’t we call this figure a square?
3.2 In the parallelogram, two opposite angles are marked x + 30° and 2 x – 10° respectively.
Explain why the marked angle is 110 ° .
3.3 The trapezium shows the two marked angles with sizes x – 20° and x + 40° respectively.
Why is this not a parallelogram?
3.4 Given is a rhombus with the short diagonal drawn; one angle made by the diagonal is 50° and one internal angle of the rhombus is marked x .
Shape sheet
Problem sheet
| LO 3 |
| Space and Shape (Geometry)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. |
| We know this when the learner: |
| 3.2 in contexts that include those that may be used to build awareness of social, cultural and environmental issues, describes the interrelationships of the properties of geometric figures and solids with justification, including: |
| 3.2.2 transformations. |
| 3.3 uses geometry of straight lines and triangles to solve problems and to justify relationships in geometric figures; |
| 3.4 draws and/or constructs geometric figures and makes models of solids in order to investigate and compare their properties and model situations in the environment; |
| 3.6 recognises and describes geometric solids in terms of perspective, including simple perspective drawing; |
| 3.7 uses various representational systems to describe position and movement between positions, including:ordered grids |
| LO 4 |
| MeasurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. |
| We know this when the learner: |
| 4.4 uses the theorem of Pythagoras to solve problems involving missing lengths in known geometric figures and solids. |
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