- Basic Concepts of Geometry
Definitions, properties and differences of points, lines, curves, straight lines, line segments, rays, collinear points and concurrent lines.
- Angles
Understand angles and their types, angle relationships, linear pairs and vertically opposite angles with clear diagrams, examples and practice problems.
- Parallel Lines
Understand parallel lines and transversals, corresponding, alternate interior and same-side interior angles with simple proofs, examples and practice.
- Triangles
Learn the parts and types of triangles, classification by sides and angles, the 180° angle-sum rule, solved examples and practice questions.
- Congruence of Triangles
Understand SSS, SAS, ASA, AAS and RHS congruence rules, corresponding parts, CPCT, solved examples and practice questions.
- Triangle Theorems
Learn isosceles, exterior-angle, angle-sum, side-angle and triangle-inequality theorems with proofs, examples and practice questions.
- Polygon Theorems
Learn the sum of interior and exterior angles of polygons and formulas for each angle of a regular polygon with easy proofs and examples.
- Theorems on Perpendicular and Oblique Segments
Learn with proofs why the perpendicular from an external point to a line is the shortest segment and how the length of an oblique segment changes with its distance from the perpendicular foot.
- Properties of a Parallelogram
Learn the important properties of a parallelogram, including equal opposite sides and angles, bisecting diagonals, congruent triangles and tests for proving a quadrilateral is a parallelogram.
- Transversal and Midpoint Theorem
Understand the Midpoint Theorem, its converse, and how parallel lines cut equal intercepts on transversals, with clear proofs and examples.
- Area Theorems of Parallelograms and Triangles
Understand the area theorems for parallelograms and triangles on the same base and between the same parallels with simple proofs and examples.
- Theorems on Concurrence in a Triangle
Understand why the perpendicular bisectors, altitudes, internal angle bisectors and medians of a triangle are concurrent, with clear proofs and examples.
- Basic Concepts of a Circle
Understand the basic parts of a circle, including centre, radius, chord, diameter, arc, semicircle, segment and sector.
- Circle Theorems on Chords and Circumcircle
Understand the unique circle through three non-collinear points and the main chord theorems using clear proofs, examples and practice questions.
- Similarity and Theorems on Similar Triangles
Important Class 10 similarity theorems including BPT and its converse, AA/AAA, SSS, SAS criteria and similarity relations formed by the altitude to the hypotenuse of a right triangle.
- Theorems on Central and Inscribed Angles
Learn the relation between central and inscribed angles, equal angles in the same segment, conditions for concyclic points and the right angle in a semicircle with proofs and examples.
- Theorems on Tangents to a Circle
Understand why a tangent is perpendicular to the radius at the point of contact, why tangents from the same external point are equal, and how the centres of touching circles are related.
- Pythagoras Theorem and Its Converse
Pythagoras theorem and its converse with proof, right-triangle formulas, Pythagorean triples, solved examples and practice questions.
