Topics
Number Systems
Number Systems
Algebra
Polynomials
Linear Equations in Two Variables
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Geometry
Introduction to Euclid’S Geometry
Lines and Angles
Triangles
Quadrilaterals
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Another Condition for a Quadrilateral to Be a Parallelogram
- The Mid-point Theorem
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Area
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral
Constructions
Mensuration
Areas - Heron’S Formula
Surface Areas and Volumes
Statistics and Probability
Statistics
Probability
notes
Look at the following figures:
In Fig. (i), trapezium ABCD and parallelogram EFCD have a common side DC. We say that trapezium ABCD and parallelogram EFCD are on the same base DC.
Similarly, in Fig.(ii), parallelograms PQRS and MNRS are on the same base SR;
In Fig.(iii), triangles ABC and DBC are on the same base BC and in Fig.(iv), parallelogram ABCD and triangle PDC are on the same base DC.
Now look at the following figures:
In Fig. (i), clearly trapezium ABCD and parallelogram EFCD are on the same base DC. In addition to the above, the vertices A and B (of trapezium ABCD) opposite to base DC and the vertices E and F (of parallelogram EFCD) opposite to base DC lie on a line AF parallel to DC. We say that trapezium ABCD and parallelogram EFCD are on the same base DC and between the same parallels AF and DC. Similarly, parallelograms PQRS and MNRS are on the same base SR and between the same parallels PN and SR [see Fig.(ii)] as vertices P and Q of PQRS and vertices M and N of MNRS lie on a line PN parallel to base SR.In the same way, triangles ABC and DBC lie on the same base BC and between the same parallels AD and BC [see Fig. (iii)] and parallelogram ABCD and triangle PCD lie on the same base DC and between the same parallels AP and DC [see Fig.(iv)].
So, two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices (or the vertex) opposite to the common base of each figure lie on a line parallel to the base.
