<p> GENERAL EDUCATION AND TRAINING CERTIFICATE</p><p>NQF LEVEL 1</p><p>ABET LEVEL 4 SITE-BASED ASSESSMENT</p><p>LEARNING AREA:MATHEMATICAL LITERACY CODE :MLMS4 TASK:PROJECT DURATION:ONE WEEK MARKS:50</p><p>This assessment task consists of 6 pages.</p><p>Copyright reserved Please turn over INSTRUCTIONS AND INFORMATION</p><p>1. The project should be completed over a period of one week – one hour per day.</p><p>2. Answer ALL the questions.</p><p>3. To complete this project you will need the following:</p><p> Pencil  Ruler  Pen  Eraser</p><p>4. ALL the drawings should be made in the ANSWER BOOK unless otherwise stated.</p><p>GEOMETRY OF 2D SHAPES (POLYGONS)</p><p>In this project you will be dealing with the following:  Classifying 2D shapes according to their sides and angles.  Solving simple geometric problems.</p><p>QUESTION 1: TRIANGLES</p><p>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:</p><p> 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°.</p><p>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</p><p>Copyright reserved Please turn over 1.1 Give the names of the following triangles:</p><p>1.1.1 (1)</p><p>1.1.2</p><p>(1)</p><p>1.2 Identify the following triangles:</p><p>1.2.1 A triangle with sides of 4 cm, 5 cm and 3 cm lengths. (1)</p><p>1.2.2 A triangle with the length of 5 cm on each side. (1)</p><p>1.2.3 A triangle with one of its angles equal to 120°. (1) [5]</p><p>QUESTION 2: ANGULAR SUM OF POLYGONS</p><p>2.1 STEP 1: Use a ruler to draw a triangle on a piece of paper.</p><p> a</p><p> b c (1)</p><p>STEP 2: Cut out the triangle and tear it into THREE PIECES so that EACH piece contains ONE angle.</p><p> b</p><p> a c (2)</p><p>STEP 3: Place the pieces together so that the VERTICES of the ANGLES meet at ONE POINT.</p><p> b a c (2)</p><p>2.2 2.2.1 Which angle was formed after fitting the three angles together? (1)</p><p>Copyright reserved Please turn over 2.2.2 What is the size of the triangle formed in QUESTION 2.2.1 above? (1)</p><p>2.2.3 What is the sum of angels of a triangle? (1)</p><p>2.2.4 What conclusion can you make based on (STEP 1–3) in QUESTION 2.1 above? </p><p>â + b + ĉ = … (1)</p><p>2.2.5 In your conclusion, which angle is equal to the sum of angels of triangles? (1) [10]</p><p>QUESTION 3: QUADRILATERALS</p><p>Quadrilaterals are POLYGONS that have FOUR SIDES and FOUR ANGLES. There are six types of quadrilaterals, namely: square; rectangles; parallelogram; rhombus; kite and trapezium.</p><p>3.1 Draw the following rectangle using a ruler in the ANSWER BOOK.</p><p>W X</p><p>Y Z (1)</p><p>3.2 Draw a diagonal line from a vertex W to a vertex Z to divide the rectangle into two triangles. (1)</p><p>3.3 Name the TWO types of triangles in which a rectangle can be divided. (2)</p><p>3.4 Complete the following:</p><p>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)</p><p>3.5 Repeat the process by drawing any other quadrilateral, for an example a rhombus. </p><p>What is your observation on the sum of angels of angles of a triangle? (4) [10]</p><p>Copyright reserved Please turn over QUESTION 4: ANY POLYGON</p><p>4.1 Study the polygon below which has been divided into triangles and complete the following sentences:</p><p>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)</p><p>4.2 Draw the following pentagon in the ANSWER BOOK.</p><p>(2)</p><p>4.3 Divide the pentagon into triangles. (1)</p><p>4.4 How many triangles did you get? (1)</p><p>4.5 What is the angular sum of a pentagon? (2) [11]</p><p>Copyright reserved Please turn over ACTIVITY 5: SOLVING GEOMETRIC PROBLEMS</p><p>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:</p><p>5.1.1 45° ; 30° ; (2)</p><p>5.1.2 65° ; 25° ; (2)</p><p>5.2 Answer the questions that follow based on QUESTION 5.1 above:</p><p>5.2.1 Give the name of the triangle in QUESTION 5.1.1 and a reason. (2)</p><p>5.2.2 What is the name of a triangle in QUESTION 5.1.2? Motivate your answer. (2)</p><p>5.3 Given a quadrilateral with the following properties:</p><p> TWO pairs of opposite angles that are equal  TWO pairs of opposite sides that are equal and parallel.</p><p>5.3.1 What is the name of this quadrilateral? (1)</p><p>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]</p><p>QUESTION 6: CONCLUSION</p><p>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.</p><p>Apply the above formula to calculate the angular sum of the following polygons:</p><p>6.1 Trapezium (1)</p><p>6.2 Pentagon (1)</p><p>6.3 Octagon (1) [3]</p><p>TOTAL: 50</p><p>Copyright reserved </p>