Academic year:
Units and Topics
| # | Unit/Topic | Marks |
|---|---|---|
| 1 | Basic Concepts in Geometry | - |
| 2 | Parallel Line | - |
| 3 | Triangles | - |
| 4 | Constructions of Triangles | - |
| 5 | Quadrilaterals | - |
| 6 | Circle | - |
| 7 | Co-ordinate Geometry | - |
| 8 | Trigonometry | - |
| 9 | Surface area and volume | - |
| Total | - |
Syllabus
1 Basic Concepts in Geometry
- Basic Concept in Geometry
- Co-ordinates of Points and Distance
- Basic concept of segment, ray and line
- Line Segment
- Ray
- Line
- Congruent Segments
- Properties of Congruent Segments
- Mid-point of a segment
- Comparison of segments
- Perpendicularity of segments or rays
- Distance of a point from a line
- Conditional Statements and Converse
- Proofs
2 Parallel Line
- Checking Parallel Lines
- 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 Triangles
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Theorem of remote interior angles of a triangle
- Remote-Interior Angles of a Triangle Theorem
- Property of an exterior angle of triangle
- Congruence of Triangles
- Isoscles Triangle Theorem
- Isoscles Triangle Theorem
- Converse of Isoscles Triangle Theorem
- Corollary
- Property of 30-60-90 Triangle Theorem
- 30-60-90 Triangle Theorem
- 45-45-90 Triangle Theorem
- Median of a Triangle
- Perpendicular bisector Theorem
- Perpendicular bisector Theorem
- Angle bisector theorem
- Properties of inequalities of sides and angles of a triangle
- Similar Triangles
4 Constructions of Triangles
- Perpendicular bisector Theorem
- Perpendicular bisector Theorem
- Construct a Triangle Given the Lengths of Its Three Sides
5 Quadrilaterals
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Types of Quadrilaterals
- 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.
- The Mid-point Theorem
6 Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- 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.
- Construction of the Incircle of a Triangle.
- Circumference of a Circle
7 Co-ordinate Geometry
8 Trigonometry
9 Surface area and volume
- Surface Area of a Cuboid
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Surface area of a sphere
- Hemisphere
- Hollow Hemisphere
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