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Homework assignment
1. The following pairs of triangles are given. State whether they are similar or not and give reasons for you answer. If the two triangles are similar, calculate the lengths of the sides not given and also the magnitudes of the angles not given in the figure.
Example:
C = F = 60°Δ ABC ΔEDF ()
AB = 4 cmAC = 5 cm (pyth)EF = 10 cm
1.1.
1.2
1.3.
1.4
2.
2.1 Complete the following:
In ΔAOB and ΔDOE:
Re a son
.......... = .......... (...........................................................................)
.......... = .......... (...........................................................................)
Δ.............. .............. ( )
2.2 Now calculate the lengths of the sides not given in the figure.
3.
3.1 Complete the following:
In Δ.......... and Δ..........
.......... = .......... (...........................................................................)
.......... = .......... (...........................................................................)
Δ.............. .............. ( )
3.2 Calculate the lengths of the following:
3.2.1 HE
3.2.2 EG
3.2.3 FJ
4. The height of a high vertical object can be determined by measuring the length of the shadow of a stick of known length and the shadow of the object. The following figures give the measurements which were made.
Determine the length of the flagpole.
ASSESSMENT TASK:
To use similarity to calculate the height of an object:
1. The following are needed:
2. You do the following:
3. Measure the following:
Results:
1. Copy the table on folio paper and complete it:
| The object of which the height is measured | The height of the eyes of the person above the ground. | Distance between the person and the point of intersection of the lines in the mirror | Distance between the point of intersection of the lines in the mirror and the object | Calculate the height of the object correct to the nearest cm |
2.
PKSLV
In the sketch PK is the height of the eyes of the person, S is the position of the mirror and VL is the height of the object, which is measured. Explain why ΔPKS ΔVLS.
3. In this task the measurements can be inaccurate. Explain which mistakes could have been made, which could influence the accuracy of the height of the object measured.
| 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 : |
| 3.1 recognises, visualises and names geometric figures and solids in natural and cultural forms and geometric settings, including:3.1.1 regular and irregular polygons and polyhedra;3.1.2 spheres;3.1.3 cylinders;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:3.2.1 congruence and straight line geometry;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; |
| 3.5 uses transformations, congruence and similarity to investigate, describe and justify (alone and/or as a member of a group or team) properties of geometric figures and solids, including tests for similarity and congruence of triangles. |
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