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GENERAL EDUCATION AND TRAINING CERTIFICATE

NQF LEVEL 1

ABET LEVEL 4 SITE-BASED ASSESSMENT

LEARNING AREA:MATHEMATICAL LITERACY CODE :MLMS4 TASK:PROJECT DURATION:ONE WEEK MARKS:50

This assessment task consists of 6 pages.

1. The project should be completed over a period of one week – one hour per day.

2. Answer ALL the questions.

3. To complete this project you will need the following:

 Pencil  Ruler  Pen  Eraser

4. ALL the drawings should be made in the ANSWER BOOK unless otherwise stated.

GEOMETRY OF 2D SHAPES (POLYGONS)

In this project you will be dealing with the following:  Classifying 2D shapes according to their sides and angles.  Solving simple geometric problems.

QUESTION 1: TRIANGLES

Triangles are polygons that consist of three sides and three angles. The angles of a triangle have specific properties that you will use in this project. The concepts are defined as follows:

 Angular sum – the sum of all the internal angles of a polygon.  Acute-angled triangle – a triangle with all the three angles acute (less than 90°)  Obtuse-angled triangle – a triangle with one angle obtuse (one angle greater than 90°)  Right-angled triangle – is a triangle in which one angle is equal to 90°.

Some triangles are named according to their sides, and these are special triangles, viz.  Isosceles triangle – triangle with two sides equal  Equilateral triangle – triangle with all three sides equal  Scalene – triangle with all three sides unequal

1.1.1 (1)

1.1.2

(1)

1.2 Identify the following triangles:

1.2.1 A triangle with sides of 4 cm, 5 cm and 3 cm lengths. (1)

1.2.2 A triangle with the length of 5 cm on each side. (1)

1.2.3 A triangle with one of its angles equal to 120°. (1) [5]

QUESTION 2: ANGULAR SUM OF POLYGONS

2.1 STEP 1: Use a ruler to draw a triangle on a piece of paper.

b c (1)

STEP 2: Cut out the triangle and tear it into THREE PIECES so that EACH piece contains ONE angle.

a c (2)

STEP 3: Place the pieces together so that the VERTICES of the ANGLES meet at ONE POINT.

b a c (2)

2.2 2.2.1 Which angle was formed after fitting the three angles together? (1)

2.2.3 What is the sum of angels of a triangle? (1)

2.2.4 What conclusion can you make based on (STEP 1–3) in QUESTION 2.1 above?

â + b + ĉ = … (1)

2.2.5 In your conclusion, which angle is equal to the sum of angels of triangles? (1) [10]

QUESTION 3: QUADRILATERALS

Quadrilaterals are POLYGONS that have FOUR SIDES and FOUR ANGLES. There are six types of quadrilaterals, namely: square; rectangles; parallelogram; rhombus; kite and trapezium.

3.1 Draw the following rectangle using a ruler in the ANSWER BOOK.

W X

Y Z (1)

3.2 Draw a diagonal line from a vertex W to a vertex Z to divide the rectangle into two triangles. (1)

3.3 Name the TWO types of triangles in which a rectangle can be divided. (2)

3.4 Complete the following:

If you divide the rectangle once with a diagonal line, it can be divided into (3.4.1) … triangles. The sum of the interior angles of a rectangle is thus equal to 2 180º = (3.4.20 … degrees. (2)

3.5 Repeat the process by drawing any other quadrilateral, for an example a rhombus.

What is your observation on the sum of angels of angles of a triangle? (4) [10]

4.1 Study the polygon below which has been divided into triangles and complete the following sentences:

The name of the figure above is (4.1.1) … (2) It can be divided into (4.1.2) … triangles. The sum of the interior angles of the figure above is thus equal to (4.1.3) 4  … = (4.1.4) … degrees. (3)

4.2 Draw the following pentagon in the ANSWER BOOK.

(2)

4.3 Divide the pentagon into triangles. (1)

4.4 How many triangles did you get? (1)

4.5 What is the angular sum of a pentagon? (2) [11]

5.1 The values of angle of a triangle are given below with one unknown angle. Calculate the third angle in each of the following triangles:

5.1.1 45° ; 30° ; (2)

5.1.2 65° ; 25° ; (2)

5.2 Answer the questions that follow based on QUESTION 5.1 above:

5.2.1 Give the name of the triangle in QUESTION 5.1.1 and a reason. (2)

5.2.2 What is the name of a triangle in QUESTION 5.1.2? Motivate your answer. (2)

5.3 Given a quadrilateral with the following properties:

 TWO pairs of opposite angles that are equal  TWO pairs of opposite sides that are equal and parallel.

5.3.1 What is the name of this quadrilateral? (1)

5.3.2 If the sum of one pair of the opposite angle is 114°, what is the sum of the other pair? (2) [11]

QUESTION 6: CONCLUSION

Let x represent the number of sides of any polygon. The formula to calculate the angular sum in terms of x of any given polygon is, AS = (x – 2) × 180°; where AS = Angular Sum.

Apply the above formula to calculate the angular sum of the following polygons:

6.1 Trapezium (1)

6.2 Pentagon (1)

6.3 Octagon (1) [3]

TOTAL: 50