ICSE Class 8 Maths, Unit 4: Geometry

What this unit aims at

The theme in this class will focus on making the definitions more meaningful and enabling children to perceive relationships between properties and figures. Logical implications and class inclusions should be understood, but the role and significance of deduction may not be understood. The children will be prepared to enter into the fourth level of geometrical thinking at this stage by learning informal deduction in this class. They learn to construct proofs, understand the role of axioms and definitions, and know the meaning of necessary and sufficient conditions. The children should be able to give reasons for steps in a proof. The another important way of learning about shapes and figures is through relating it with numbers i.e using the analytical geometry. Initiation of this process will be i done in this class with introduction of representing any point in a plane as ordered pair o

Your child should be able to

• explore and verify properties of quadrilaterals like sum of angles of a quadrilateral is equal to 360° (by verification)
• explore and verify properties of parallelogram (by verification) like (i) opposite sides of a parallelogram are equal, (ii) opposite angles of a parallelogram are equal, (iii)diagonals of a parallelogram bisect each other. [ also find justification to why (iv), (v) and (vi) follow from (ii)] (iv) diagonals of a rectangle are equal and bisect each other (v) diagonals of a rhombus bisect each other at right angles. (vi) diagonals of a square are equal and bisect each other at right angles. identify and match pictures with objects [more complicated e.g. nested, joint 2-D and 3-D shapes (not more than 2)]
• draw 2-D representation of 3-D objects (continued and extended)
• count number of vertices, edges & faces & verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)
• generalize the sum of angles of quadrilateral and use it in solving various problems related to finding angles of a quadrilateral
• explain properties of parallelograms and tries to reason out how one property is related to other
• represent 3-D shapes on a plan surface like paper, board, wall etc
• make nets of prisms and pyramids and forms the shapes from the nets
• construct quadrilaterals using pair of compasses and straight edge given:
• four sides and one diagonal three sides and two diagonals

Key concepts in this unit

• Understanding shapes:
• Properties of quadrilaterals –
• Angle Sum property Properties of parallelogram (By verification) (i) Opposite sides of a parallelogram are equal, (ii) Opposite angles of a parallelogram are equal, (iii)
• Diagonals of a parallelogram bisect each other. (iv)
• Diagonals of a rectangle are equal and bisect each other.
• (v) Diagonals of a rhombus bisect each other at right angles. (vi) Diagonals of a square are equal and bisect each other at right angles.
• Representing 3-D in 2-D Identify and match pictures with objects [more complicated e.g. nested, joint 2-D and 3-D shapes (not more than 2)].
• Drawing 2-D representation of 3-D objects (Continued and extended)
• Counting vertices, edges & faces & verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)
• Construction of Quadrilaterals:
• Given four sides and one diagonal
• Three sides and two diagonals
• Three sides and two included angles
• Two adjacent sides and three angles
• Idea of reflection symmetry and symmetrical shapes
• Circle Circle, centre, radius/ diameter, arc, chord, sector and segment.