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Grade 9
Geometry
Triangles
Congruence of Triangles
Grade 9
1.
Number System
1.1.
Rational and Irrational Numbers
1.1.1.
Revisiting Concepts
1.1.2.
Without Actual Division Identify Terminating Decimals
1.1.3.
Relate Rational Numbers and Decimals
1.1.3.1.
Express Rational Numbers as Terminating and Recurring Decimals
1.1.3.2.
Express Terminating and Recurring Decimals as Rational Numbers
1.1.4.
Represent Rational/Irrational Numbers on the Number Line
1.1.5.
Find Rational/Irrational Numbers Between Given Rational/Irrational Numbers
1.1.6.
Identify Rational and Irrational Numbers
1.2.
Real Numbers
1.2.1.
Addition and Subtraction of Real Numbers
1.2.2.
Multiplication and Division of Real Numbers
1.2.3.
Real Numbers: Mixed Operations (Simplification)
1.2.3.1.
Simplify and Find Values of Expressions using Rationalization
1.2.3.2.
Simplify Expressions Using the Laws of Radicals
2.
Polynomials
2.1.
Introduction to Polynomials
2.2.
Evaluate Polynomials
2.3.
Zeros of a Polynomial
2.4.
Remainder Theorem
2.5.
Factor Theorem
2.6.
Factorization of Polynomials
2.6.1.
Factorization by Taking out the Common Factors
2.6.2.
Factorization by Grouping
2.6.3.
Factorization When the Expression is a Difference of Two Squares
2.6.4.
Factorization of Quadratic Polynomials
2.6.5.
Factorization of Sum or Difference of Cubes
2.6.6.
Factorization of Cubic and Biquadratic Polynomials
2.7.
Evaluate Polynomials Using Algebraic Identities
3.
Geometry
3.1.
Introduction to Euclid's Geometry
3.1.1.
Euclid's Axioms and Postulates
3.1.2.
Revisiting Basic Concepts of Geometry
3.2.
Angles and Lines
3.2.1.
Understanding Basic Terms
3.2.2.
Categorize Angles on the Basis of Their Measures
3.2.3.
Angles Around a Point
3.2.4.
Complementary and Supplementary Pairs of Angles
3.2.5.
Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles
3.2.6.
Parallel Lines, Transversal, and Angles Formed
3.3.
Triangles
3.3.1.
Classification of Triangles on the Basis of its Sides and Angles
3.3.2.
Theorems and Problems Related to Side and Angle Measures of Triangles
3.3.3.
Congruence of Triangles
3.3.3.1.
Congruence: Understand the Meaning and Criteria
3.3.3.2.
Problems Related to Congruence of Triangles
3.3.4.
Inequalities in a Triangle
3.4.
Quadrilaterals and Parallelograms
3.4.1.
Understand the Concept of Quadrilaterals and Related Terms
3.4.2.
Theorems and Problems Related to the Angles of a Quadrilateral
3.4.3.
Theorems and Problems Related to Parallelograms
3.4.4.
Intercept Theorem and Midpoint Theorem
3.5.
Circles
3.5.1.
Terms Related to Circles
3.5.2.
Theorems and Problems Related to Chord Properties of Circles
3.5.3.
Theorems and Problems Related to Angles Subtended by Arcs/Chords
3.5.4.
Theorems and Problems Related to Cyclic Quadrilaterals
3.5.5.
Problems Related to Circumcircles and In-circles
4.
Coordinate Geometry
4.1.
Understand the Terms Related to Coordinate Geometry
4.2.
Identify the Coordinates and the Quadrants
4.3.
Draw the Graphs of Linear Equations
4.4.
Higher Order Thinking Skills (HOTS) Related to the Cartesian Plane
5.
Linear Equations in Two Variables
5.1.
Solution of Linear Equations in Two Variables
5.2.
Finding the Unknowns
5.3.
Graph of Linear Equations in Two Variables
5.4.
Word Problems
6.
Mensuration
6.1.
Measurement of Areas
6.1.1.
Measuring Areas of Triangles
6.1.1.1.
Area of a Triangle Using Base and Altitude
6.1.1.2.
Area of a Triangle Using Heron's Formula
6.1.2.
Measuring Areas of Quadrilaterals
6.1.2.1.
Area of a Quadrilateral
6.1.2.2.
Area of a Parallelogram
6.1.2.3.
Area of a Rhombus
6.1.2.4.
Area of a Trapezium
6.1.2.5.
Area of a Quadrilateral Using Heron's Formula
6.1.2.6.
Application of Results on Area of Polygonal Regions
6.2.
Volume and Surface Area
6.2.1.
Volume and Surface Area of Cuboids and Cubes
6.2.2.
Volume and Surface Area of Cylinders
6.2.3.
Volume and Surface Area of Circular Cones
6.2.4.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
6.2.5.
Mixed Problems on Volume and Surface Area
7.
Statistics and Probability
7.1.
Statistics
7.1.1.
Frequency Distribution of Grouped and Ungrouped Data
7.1.2.
Cumulative Frequency Table of an Ungrouped Data
7.1.3.
Bar Graph
7.1.3.1.
Creating Bar Graphs
7.1.3.2.
Interpreting Bar Graphs
7.1.4.
Histogram
7.1.5.
Frequency Polygon
7.1.6.
Mean, Median, and Mode
7.1.6.1.
Mean
7.1.6.1.1.
Problems on Mean
7.1.6.1.2.
Mean for Ungrouped Frequency Distributions
7.1.6.2.
Median for Ungrouped Data
7.1.6.3.
Mode for Ungrouped Data
7.2.
Probability
7.2.1.
Calculate Probability for Events in Random Experiments
Grade 9 Pakistan School Math
Congruence of Triangles
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Triangles
Pakistan