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
notes
Congruence of Triangles:
Two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
△ ABC and △ PQR have the same size and shape. They are congruent.
△ABC ≅ △PQR
This means that, when you place △PQR on △ABC, P falls on A, Q falls on B and R falls on C, also PQ falls along `bar"AB", bar"QR" "falls along" bar"BC" and bar"PR" "falls along" bar"AC"`.
If, under a given correspondence, two triangles are congruent, then their corresponding parts (i.e., angles and sides) that match one another are equal.
Thus, in these two congruent triangles.
We have:

Corresponding vertices: A and P, B and Q, C, and R.

Corresponding sides: `bar"AB" and bar"PQ", bar"BC" and bar"QR", bar"AC" and bar"PR"`.

Corresponding angles: ∠A and ∠P, ∠B and ∠Q, ∠C, and ∠R.
Congruent triangles corresponding parts in short ‘CPCT’ stands for corresponding parts of congruent triangles.
Example
∆ABC and ∆PQR are congruent under the correspondence:
ABC ↔ RQP
Write the parts of ∆ABC that correspond to
(i) `bar"PQ"`
(ii)∠Q
(iii) `bar"RP"`
For a better understanding of the correspondence, let us use a diagram
The correspondence is ABC ↔ RQP.
This means A ↔ R; B ↔ Q; and C ↔ P.
So,
(i) `bar"PQ" ↔ bar"CB"`
(ii) ∠Q ↔ ∠B and
(iii) `bar"RP" ↔ bar"AC"`.