Topics
Basic Concepts in Geometry
 Introduction to Basic Concepts in Geometry
 Concept of Points
 Concept of Line
 Concept of Plane
 Coordinates of Points and Distance
 Betweenness
 Concept of Line Segment
 Concept of Ray
 Conditional Statements and Converse
 Proofs
Parallel Line
 Parallel Lines
 Checking Parallel Lines
 Pairs of Lines  Transversal of Parallel Lines
 Properties of Parallel Lines
 Interior Angle Theorem
 Corresponding Angle Theorem
 Alternate Angles Theorems
 Use of properties of parallel lines
 Test for Parallel Lines
 Interior Angles Test
 Alternate Angles Test
 Corresponding Angles Test
 Corollary of Parallel Lines
Triangles
 Concept of Triangles  Sides, Angles, Vertices, Interior and Exterior of Triangle
 Remote Interior Angles of a Triangle Theorem
 Exterior Angle of a Triangle and Its Property
 Congruence of Triangles
 Isosceles Triangles Theorem
 Converse of Isosceles Triangle Theorem
 Corollary of a Triangle
 Property of 30° 60° 90° Triangle Theorem
 Property of 45° 45° 90° Triangle Theorem
 Median of a Triangle
 Property of Median Drawn on the Hypotenuse of Right Triangle
 Perpendicular Bisector Theorem
 Angle Bisector Theorem
 Properties of inequalities of sides and angles of a triangle
 Similar Triangles
 Similarity of Triangles
Constructions of Triangles
 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.
Quadrilaterals
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 Properties of a Parallelogram
 Properties of Rhombus
 Properties of a Square
 Properties of Rectangle
 Properties of Trapezium
 Property: The Opposite Sides of a Parallelogram Are of Equal Length.
 Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
 Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
 Property: The adjacent angles in a parallelogram are supplementary.
 Tests for Parallelogram
 Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
 Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
 Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
 Theorem: If One Pair of Opposite Sides of a Quadrilateral Are Equal and Parallel, It is a Parallelogram.
 Property: The Diagonals of a Rectangle Are of Equal Length.
 Property: Diagonals of a Square Are Congruent.
 Property: The diagonals of a square are perpendicular bisectors of each other.
 Property: Diagonals of a Square Bisect Its Opposite Angles.
 Property: The diagonals of a rhombus are perpendicular bisectors of one another.
 Property: Diagonals of a Rhombus Bisect Its Opposite Angles.
 Properties of Isosceles Trapezium
 Theorem of Midpoints of Two Sides of a Triangle
 Converse of Midpoint Theorem
Circle
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Properties of Chord
 Theorem: a Perpendicular Drawn from the Centre of a Circle on Its Chord Bisects the Chord.
 Theorem : 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
 Properties of Congruent Chords
 Theorem: Equal chords of a circle are equidistant from the centre.
 Theorem : The Chords of a Circle Which Are Equidistant from the Centre Are Equal.
 Incircle of a Triangle
 Construction of the Incircle of a Triangle.
 Circumcentre of a Triangle
 Construction of the Circumcircle of a Triangle
Coordinate Geometry
 Coordinate Geometry
 The Coordinates of a Point in a Plane
 Coordinates of Points on the Axes
 Plotting a Point in the Plane If Its Coordinates Are Given.
 Equations of Lines Parallel to the Xaxis and Yaxis
 Graphs of Linear Equations
 The Graph of a Linear Equation in the General Form
Trigonometry
 Trigonometry
 Terms Related to Right Angled Triangle
 Trigonometric Ratios and Its Reciprocal
 Relation Among Trigonometric Ratios
 Trigonometric Ratios of 30° and 60° Angles
 Trigonometric Table
 Important Equation in Trigonometry
Surface area and volume
 Ray
 Perpendicularity of rays
Definition
Rays: A ray is part of a line that extends without end in one direction.
Notes
Ray:

A ray is part of a line that extends without end in one direction. It starts from one endpoint and extends forever in one direction.

A ray has only one endpoint.
 A ray starting from point A and passing through P is denoted by `vec(AP)`.
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