CLASS VI
CLASS VII
CLASS VIII
Understanding Elementary
Shapes (2-D and 3-D)
Symmetry: (reflection)
Constructions (using Straight edge Scale,protractor, compasses)
Basic geometrical ideas (2 -D)
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Measure of Line segment
Measure of angles
Pair of lines
Intersecting and perpendicular lines
Parallel lines
Types of angles- acute, obtuse,
right, straight, reflex, complete and zero angle
Classification of triangles (on the
basis of sides, and of angles)
Types of quadrilaterals –
Trapezium, parallelogram, rectangle, square, rhombus.
Simple polygons (introduction)
(Upto octagons regulars as well as non regular)
Identification of 3-D shapes: Cubes,
Cuboids, cylinder, sphere, cone, prism (triangular), pyramid
(triangular and square) Identification and locating in the
surroundings
Elements of 3-D figures. (Faces,
Edges and vertices)
Nets for cube, cuboids, cylinders,
cones and tetrahedrons.
Observation and identification
of 2-D symmetrical objects for
reflection symmetry
Operation of reflection (taking
mirror images) of simple 2-D objects
Recognising reflection symmetry
(identifying axes)
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• Drawing of a line segment
• Construction of circle
• Perpendicular bisector
• Construction of angles (using protractor)
Angle 60°, 120° (Using
Compasses)
Angle bisector- making angles
of 30°, 45°, 90° etc. (using compasses)
Angle equal to a given angle
(using compass)
Drawing a line perpendicular to
a given line from a point a) on the line b) outside the line.
Understanding shapes
Properties of triangles
Symmetry
Representing 3-D in 2-D
Construction (Using scale,
protractor, compass)
Congruence
Pairs of angles (linear,
supplementary, complementary, adjacent, vertically opposite)
(verification and simple proof of vertically opposite angles)
Properties of parallel lines with
transversal (alternate, corresponding, interior, exterior
angles)
Angle sum property (with
notions of proof & verification through paper folding, proofs
using property of parallel lines, difference between proof and
verification.)
Exterior angle property
Sum of two sides of a it’s
third side
Pythagoras Theorem
(Verification only)
Recalling reflection symmetry
Idea of rotational symmetry,
observations of rotational symmetry of 2-D objects. ( 90, 120, 180 degrees)
Operation of rotation through 90 and 180 degrees of simple figures.
Examples of figures with both
rotation and reflection symmetry (both operations)
Examples of figures that have
reflection and rotation symmetry and vice-versa
Drawing 3-D figures in 2-D
showing hidden faces.
Identification and counting of
vertices, edges, faces, nets (for cubes cuboids, and cylinders,
cones).
Matching pictures with objects
(Identifying names)
Mapping the space around
approximately through visual estimation.
Congruence through
superposition (examples blades, stamps, etc.)
Extend congruence to simple
geometrical shapes e.g. triangles, circles
Criteria of congruence (by
verification) SSS, SAS, ASA, RHS
Construction of a line parallel to
a given line from a point outside it.(Simple proof as remark with
the reasoning of alternate angles)
Construction of simple triangles.
Like given three sides, given a side and two angles on it, given
two sides and the angle between them.
Representing 3-D in 2-D
Understanding shapes:
Properties of parallelogram (By
verification)
Properties of quadrilaterals –
Sum of angles of a quadrilateral is equal to 360 degrees (By verification)
Opposite sides of a
parallelogram are equal,
Opposite angles of a
parallelogram are equal,
Diagonals of a parallelogram
bisect each other. [Why (iv), (v)
and (vi) follow from (ii)]
Diagonals of a rectangle are
equal and bisect each other.
Diagonals of a rhombus bisect
each other at right angles.
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)].
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
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Line, line segment, ray.
Open and closed figures.
Interior and exterior of closed figures.
Curvilinear and linear boundaries
Angle — Vertex, arm, interior
and exterior,
Triangle — vertices, sides, angles, interior and exterior, altitude and median
Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
Circle — Centre, radius,
diameter, arc, sector, chord segment, semicircle, circumference,
interior and exterior