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Number Systems
Number Systems
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Linear Equations in Two Variables
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
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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
 Another Condition for a Quadrilateral to Be a Parallelogram
 Theorem of Midpoints of Two Sides of a Triangle
 Property: The Opposite Sides of a Parallelogram Are of Equal Length.
 Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
 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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