Academic year:
Topics with syllabus and resources
1.00 Basic Concepts in Geometry
 Basic Concept in Geometry
 Point
 Plane
 Line
 Coordinates of points and distance
 Betweenness
 Basic concept of segment, ray and line
 Line Segment
 Ray
 Line
 Congruent Segments
 Properties of Congruent Segments
 Midpoint of a segment
 Comparison of segments
 Perpendicularity of segments or rays
 Distance of a point from a line
 Conditional Statements and Converse
 Proofs
2.00 Parallel Line
 Concept of Parallel Line
 Line and Line Segments
 Parallel Lines
 Intersecting Lines
 Transversal
 Concept for Properties of Parallel Lines with Transversal
 Interior angle theorem
 Corresponding angles and alternate angles theorem
 Use of properties of parallel lines
 Test for Parallel Line
 Interior angles test
 Alternate angles test
 Corresponding angle test
3.00 Triangles
 Concept of Triangles
 Theorem of remote interior angles of a triangle
 RemoteInterior Angles of a Triangle Theorem
 Property of an exterior angle of triangle
 Congruence of Triangles
 Properties of Congruent Triangle
 ASA Test
 SAS Test
 SSS Test
 Hypotenuse Side Test
 Corresponding angles of congruent triangles
 Isoscles Triangle Theorem
 Isoscles Triangle Theorem
 Converse of Isoscles Triangle Theorem
 Corollary
 Property of 306090 Triangle Theorem
 306090 Triangle Theorem
 454590 Triangle Theorem
 Median of a Triangle
 Property of median drawn on the hypotenuse of right triangle
 Perpendicular bisector Theorem
 Perpendicular bisector Theorem
 Angle bisector theorem
 Properties of inequalities of sides and angles of a triangle
 Similar Triangle
4.00 Constructions of Triangles
 Perpendicular bisector Theorem
 Perpendicular bisector Theorem
 Construction of Triangles

To construct a triangle when its base, an angle adjacent to the base and the sum of the lengths of remaining sides is given.

To construct a triangle when its base, angle adjacent to the base and difference between the remaining sides is given.

To construct a triangle, if its perimeter, base and the angles which include the base are given.

5.00 Quadrilaterals
 Concept of Quadrilaterals
 Types of Quadrilaterals
 Parallelogram
 Opposite sides and opposite angles of a parallelogram are congruent.
 Diagonals of a parallelogram bisect each other.
 If a pair of opposite sides of a quadrilateral are equal and parallel, it is a parallelogram.
 Parallelogram
 Tests for parallelogram
 If pairs of opposite sides of a quadrilateral are congruent then that quadrilateral is a parallelogram.
 If both the pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram.
 If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
 A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
 Properties of Rhombus
 Diagonals of a rhombus are perpendicular bisectors of each other.
 Properties of Square
 Diagonals of a square are congruent.
 Properties of Rectangle
 Diagonals of a rectangle are congruent.
 The Midpoint Theorem
 Theorem of midpoints of two sides of a triangle : The line segment joining the midpoints of any two sides of a triangle is parallel to the third side, and is equal to half of it.
 Converse of midpoint theroem : The straight line drawn through the midpoint of one side of a triangle parallel to another, bisects the third side.
 Theorem of midpoints of two sides of a triangle : The line segment joining the midpoints of any two sides of a triangle is parallel to the third side, and is equal to half of it.
6.00 Cirle
 Concept of Circles
 Circle
 Centre of the circle
 Radius
 Chord
 Diameter
 Concentric Circle
 Properties of Chord
Properties of congruent chords:
 A perpendicular drawn from the centre of a circle on its chord bisects the chord.

The segment joining the centre of a circle and the midpoint of its chord is perpendicular to the chord.
Relation between congruent chords of a circle and their distances from the centre

Congruent chords of a circle are equidistant from the centre of the circle.

The chords of a circle equidistant from the centre of a circle are congruent.
 Incircle Of a triangle
 Circumcircle of circle
7.00 Coordinate Geometry
8.00 Trigonometry
9.00 Surface area and volume