Basic Concepts in Geometry
- 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
- 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.
- 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 Mid-point Theorem
- 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
- The Co-ordinates of a Point in a Plane
- Co-ordinates of Points on the Axes
- Plotting a Point in the Plane If Its Coordinates Are Given.
- Equations of Lines Parallel to the X-axis and Y-axis
- Graphs of Linear Equations
- The Graph of a Linear Equation in the General Form
Surface area and volume
Plane: Plane is a flat surface on which a straight line joining any two points on it would wholly lie.
In mathematics, a flat surface is called a plane.
Each flat surface is a part of an infinite surface.
- Plane is a flat surface on which a straight line joining any two points on it would wholly lie.
Even though we draw a suitably small figure of the plane, it actually extends infinitely on all sides. Arrows are drawn to show that the plane extends infinitely in all directions. However, these arrows are often omitted for the sake of convenience.
The 2-dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width. Two-dimensional or 2-D shapes do not have any thickness and can be measured in only two faces.
A plane figure can be made of straight lines, curved lines, or both straight and curved lines. The circle, the square, the rectangle, the quadrilateral and the triangle are examples of plane figures.