Construct a trapezium ABCD where AB||CD, AD = BC = 3.2cm, AB = 6.4 cm and CD = 9.6 cm. Measure ∠B and ∠A. [Hint : Difference of two parallel sides gives an equilateral triangle.] 1 : Constructing a Tessellation Tessellation: A tessellation is created when a shape is repeated over and over again covering a plane surface without any gaps or overlaps. Regular Tesselations : It means a tessellation made up of congruent regular polygons. For example: A tessellation of triangles This arrangement can be extended to complete tiling of a floor (or tessellation). Rules for Regular Tessellation: (i) In tessellation there should be no overlappings/gaps between tiles. (ii) The tiles must be regular polygons. (iii) Design at each vertex must look the same. Caution Will pentagons work? The interior angle of a pentagon is 1080 . . . 1800 + 1080 + 1080 = 3240 degrees . . . No! Thus, since the regular polygons must fill the plane at each vertex, the interior angle must be an exact divisor of 360°. Now, find the regular polygon that can tessellate by trying a sample in table below. Polygon Tessellation 1. Triangle 2. Square 3. Regular Pentagon 4. Regular Hexagon 5. Regular Heptagon 6. Regular Octagon Conclusion Thus, only regular polygons that can tessellate are 1. ______________________ 2. ______________________ 3. ______________________ Assignment 1. You can construct a tessellation on computer using following steps: - Hold down a basic images and copy it to paintbrush. - Keep on moving and pasting by positioning each to see a tessellation. 2. Semi Regular Tessellation : These are made by using two or more different regular polygons. Every vertex must have the same configuration, e.g.: Y - yellow B - Blue G - Green R - Red Now discover same more tessellation of this type . 2 Constructing a TANGRAM Cut the pieces of given square as shown on next page and make different shapes as shown below. Different shapes can be made of Tangram Pieces Try to form a story using different shapes of animals. Required Square 3 Motivate the students to participate Read the following description of a square before the students and let them draw what you have described. Descriptions: My quadrilateral has opposite sides equal. Let students compare their drawings with each other and with your square. Let students discuss what all their drawings have in common (they are all parallelograms) and what additional information is necessary to guarantee that they all would draw a square. (e.g. All 4 sides equal and one right angle.) 4: Place ‘’ or ‘’ in the appropriate spaces according to the property of different quadrilaterals. Parallelogram Rectangle Rhombus Square Trapezium Trapezium Kite with non parallel sides equal Opposite sides parallel Opposite sides equal Opposite angles equal Diagonal forms congruent triangles Diagonals bisect each other Diagonals are perpen- dicular Diagonals are equal Diagonals bisect opposite angles All angles are right All sides are equal Use the quadrilateral chart at Page 167 to do the following activity and answer the following questions.
- (a)How can you use the properties shown in the quadrilateral chart to make a statement that you believe is true about all parallelograms?
- (b)How can you use the properties shown in the quadrilateral chart to make a statement that you believe is true about all rhombuses?
- (c)How can you use the properties shown in the quadrilateral chart to make a statement that you believe is true about all rhombuses, but not parallelograms?
- (d)How can you use the properties shown in the quadrilateral chart to make a statement that you believe is true about only rhombuses? (e) How are the properties of rhombuses like the properties of parallelograms in general? (f) How are the properties of rhombuses different from the properties of parallelograms? (g) Which quadrilaterals have exactly one line of symmetry? Exactly two? Exactly three? Exactly four? (h) Make a ‘Family Tree’ to show the relationship among the quadrilaterals you have been investigating. 5: Have students take each of the quadrilateral named below, join, in order, the mid points of the sides and describe the special kind of quadrilaterals they get each time: (a) Rhombus. (b) Rectangle. (c) Trapezium with non-parallel sides equal. (d) Trapezium with non-parallel sides unequal. (e) Kite. 6: Crossword Puzzle Solve the given crossword and then fill up the given boxes (on the next page). Clues are given below for across as well as downward filling. Also, for across and down clues, clue number is written at the corner of the boxes. Answers of clues have to be filled up in their respective boxes. Clues Across 1. A quadrilateral with pair of parallel sides. 2. A simple closed curve made up of only line segments. 3. A quadrilateral which has exactly two distinct consecutive pairs of sides of equal length. 4. A line segment connecting two non-consecutive vertices of a polygon. 5. The diagonals of a rhombus are _________ bisectors of one another. 6. The ___________ sides of a parallelogram are of equal length. 7. The number of sides of a regular polygon whose each exterior angle has a measure of 450. 8. The sum of measure of the three angles of a _________________ is 1800. 9. A polygon which is both equiangular and equilateral is called a _________ polygon. 10. Number of sides of a nonagon. Down 11. Name of the figure 12. The ___________ angles of a parallelogram are supplementary. 13. A ______________ is a quadrilateral whose pair of opposite sides are parallel. 14. The diagonals of a rectangle are of _______________ length. 15. A five sided polygon. 16. The diagonals of a parallelogram _____________ each other. 17. A quadrilateral having all the properties of a parallelogram and also that of a kite. MATHEMATICS