Curriculums/Geometry

10th GRADES

 

Chapter 1:  Basic Geometric Concepts
Term, proposition, proof, theorem, postulate
Point, line, plane
Distance between two points
Line segment, Ray, Betweennes
Position of a line and a plane with respect to each other
Position of two planes

Chapter 2: Angles
Congruence of angles
Interior and exterior regions of an angle
Measure of an angle
Types of an angles
Angles formed by parallel lines and transversal
Angles with parallel arms
Angles with corresponding perpendicular arms

Chapter 3: Geometrical Transformations in A Plane
Dilemma
Symmetry
Rotation

Chapter 4: Concept of Polygon and Triangle
Elements and auxiliary elements of triangle
Types of triangles
Angles of triangles
Relation among sides and angles of a triangles
Triangle inequality
Construction ot triangles
Concept of congruence triangles
Congruence postulate of triangles
Congruence theorems of triangles

Chapter 5: Similarity
Ratio and proportion
Similar polygons, similar triangles
Scale factor
Similarity postulate of triangles
Triangle proportionality theorem and its converse
Angle bisector theorem
Angle-angle-angle similarity theorem
Thales theorem
Menelaus theorem
Seva theorem
Side-side-side similarity theorem
Metric relations in right triangles
The Pythagorean theorem

Chapter 6: Analiticy of Line
Elements of coordinate plane
Graph of linear equations
Distance formula
Midpoint formula
Slope of a line
Equation of a line
Equation for angle bisector
Point dividing a line segment proportionally
Slope of angle between two lines
Distance between two lines

 

  

 11th GRADES  

 

 

UNIT 1: POLYGONS

 

Introduction to polygons, Curves and the concept of polygons

Basic properties of convex polygons

Regular polygons

Quadrilaterals and their basic properties

Trapezoids

Parallelograms

Rhombi and rectangles

Squares and Kites

 

UNIT 2: CIRCLES

 

The concept of circle fundamental concepts of the circle                

Corresponding position of a line and a circle in the same plane

Properties related to chords of a circle.

Properties of tangents of a circle

Corresponding position of two circles

Arcs and angels of the circle

Circumference and arc length of circles                       

Calculation of tangent lengths of circles

Power of a point

Circles of triangle                                               

Inscribed and circumscribed quadrilaterals

 

UNIT 3: ANALYTIC ANALYSIS OF CIRCLE

 

Equation of circle, parametric equation of circle

Construction of a circle whose equation is given

Equation of circle whose three points are given

Corresponding positions of a line and a circle

Equations of Tangents and Normals

 

UNIT 4: AREAS OF POLYGONAL REGIONS

 

Concept of polygonal regions Area of triangular regions

Area of triangular regions

Properties related to area of triangles and some conclusions

Areas of quadrilaterals

Area of some special quadrilaterals

Area of regular polygons

Area of circles, sectors, segments and rings

Area of segments and rings

Area of circles and sectors, segments and rings

  

 

 

 12th GRADES

 

 

Unit 1: AREAS AND VOLUMES OF SOLIDS

 

Prisms                                                                    

Regular, rectangular, right and oblique prisms

Area and volume of prism                                    

Cavalier's Principle                                               

Cylinders                                                                

Right cylinder and oblique cylinder                    

Area and volume of a cylinder                            

Pyramids                                                                

Regular pyramid                                                   

Regular tetrahedron, regular Octahedron        

Area and volume of a pyramid                            

Area and volume of Frustum of a pyramid       

                                                                          

Cones                                                                

Right and oblique cone                                  

Area and volume of a cone                             

Area and volume of a Frustum of a cone     

                                                                           

Spheres                                                            

Corresponding position  and  crossection     

Determination of a sphere                             

Area of Zone, Lune and spherical segment 

Volume of spherical segment and Wedge    

  

Unit 2: ANALYTICAL ANALYSIS OF THE CONES

                                 

ELLIPSE                                                               

Definition of ellipse and the axes of the ellipse  

Eccentricity of the ellipse                                      

Equation of the ellipse with center of the origin

Equation of the tangent and the normal         

Parametric equation of the ellipse                  

 

HYPERBOLA                                                   

Definition of hyperbola                                     

Eccentricity of the hyperbola                                              

Equation of the hyperbola with center at the origin         

Equation of the tangent and the normal       

Asymptotes of the hyperbola                        

Rectangular hyperbola

                        

PARABOLA                                          

Definition of parabola                          

Focus and directrix of a parabola      

Equations of the tangent and the normal an

 

Unit 3: VECTORS                              

 

Vectors in space, analytical analysis of the line and the plane  

Position vector                                      

The vector determined by two points

Norm of the vector and unit vector                              

Operations on the set of vectors         

Multiplication of the vectors by scalars       

Linear combination of vectors (dependence and independence)

Parallel vectors, inner product function                                                                                                        

Euclidean inner product, Schwarz inequality   

                                                                              

Unit 4: MATRICES               

 

Definition of a matrix                              

Operation with matrices                         

Addition, subtraction, multiplication of matrices  

Properties of matrix multiplication      

Identity matrix                                       

Transpose of a matrix                             

Properties of transposes                         

Inverse of a matrix by Gaussian Jordan method   

                                                                                   

Unit 5: DETERMINANTS        

 

Minors and cofactors of a matrix  

Properties of Determinant            

Determinant of a transpose           

Ad joint of a matrix                            

Determinant and inverse of a matrix     

Determinant of a transpose                                                                              

 

SYSTEMS OF LINEAR EQUATIONS

 

Solution set of a system of linear equations          

Methods of solution of system of linear equations    

Cramer's rule