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 Midpoint 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
definition
Quadrilaterals: A foursided polygon is a quadrilateral. Any four points in a plane, out of which three are noncollinear are joined in order to formed a foursided closed figure called ‘quadrilateral’.
notes
Quadrilaterals:
 Any four points in a plane, out of which three are noncollinear are joined in order to formed a foursided closed figure called ‘quadrilateral’.
 A quadrilateral has four sides, four angles and four vertices. Quadrilateral could be regular or irregular.

A foursided polygon is a quadrilateral.
 Quadrilateral ABCD has four sides `bar"AB", bar"BC", bar"CD", and bar"DA"`.
 It has four angles ∠A, ∠B, ∠C, and ∠D.
 A, B, C and D are the four vertices and
 BD and AC are the two diagonals of the quadrilateral ABCD.
Reading and Writing of a Quadrilateral:

A quadrilateral can be named by starting at any vertex and going serially either clockwise or anticlockwise around the figure.

When writing the name of a quadrilateral a sign like this ‘□’ is put in place of the word ‘quadrilateral’.
Clockwise  Anticlockwise  
Reading  Writing  Reading  Writing 
Quadrilateral MNOP  □ MNOP  Quadrilateral PONM  □ PONM 
Quadrilateral NOPM  □ NOPM  Quadrilateral ONMP  □ ONMP 
Quadrilateral OPMN  □ OPMN  Quadrilateral NMPO  □ NMPO 
Quadrilateral PMNO  □ PMNO  Quadrilateral MPON  □ MPON 
1. Adjacent Sides of a Quadrilateral:
 Adjacent sides of the quadrilateral have a common vertex.
 The sides MN and MP of □ MNOP have a common vertex M. Sides MN and MP are adjacent sides.
 Every quadrilateral has four pairs of adjacent sides.
Pairs of adjacent sides:

Side MN and Side MP

Side MN and Side NO

Side NO and Side OP

Side OP and Side MP.
2. Opposite Sides of a Quadrilateral:
 Opposite sides of the quadrilateral do not have a common vertex.
 In □ MNOP the sides MP and NO have no common vertex.
 Side MP and side NO are opposite sides of the quadrilateral.
Pairs of opposite sides:

sides MP and NO

sides MN and PO
3. Adjacent Angles of a Quadrilateral:
 The angles of a quadrilateral which have one common arm are called adjacent angles of the quadrilateral.
 These angles are neighbouring or adjacent angles.
Name the adjacent angles of the quadrilateral MNOP.

∠MNO and ∠PMN

∠MPO and ∠NOP

∠PON and ∠MNO

∠ONM and ∠PMN
4. Opposite Angles of a Quadrilateral:
 The angles of a quadrilateral which do not have a common arm are called opposite angles of a quadrilateral.
 They lie opposite to each other.
Pair of Opposite angle:
 Angle opposite to ∠PMN is ∠NOP.
 Angle opposite to ∠MNO is ∠OPM.
5. Diagonals of a Quadrilateral:
 The line segments which join the vertices of the opposite angles of a quadrilateral are the diagonals of the quadrilateral.
 The segments MO and NP are the diagonals of the quadrilateral ABCD.
6. Interior & Exterior of A Quadrilateral:
 Being a polygon, a quadrilateral has an exterior and an interior.
 P, Q, and R are in the interior of the quadrilateral, M and L are in the exterior, and A, B, C, D, and E on the quadrilateral.
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