USA - Geometry - Syllabus

  • Geometry Syllabus – Common core curriculum

    1. Lines and Angles
      • Line
      • Line segment and Ray
      • Angle
      • Type of angles
    2. Parallel Lines
      • Transversal
      • Parallel lines and relation between different angles formed by transversal and parallel lines
    3. Triangles
      • Triangle
      • Basic properties of triangle
      • Angle sum property and different types of Triangles
    4. Congruence of triangles
      • Congruency
      • SSS, SAS, ASA, AAS and RHS congruency of triangles
    5. Concurrent lines in Triangles
      • Median-Centroid
      • Altitude-Orthocentre
      • Angular bisector-Incentre.
    6. Polygons
      • Polygon
      • Different types of Polygons
      • Interior angle Sum
      • Exterior angle sum and No.Of diagonals.
    7. Quadrilaterals
      • Quadrilateral
      • Angle sum properties of Quadrilateral and basic properties of Quadrilateral.
      • Types of Quadrilateral
      • Quadrilateral
      • Trapezium
      • Parallelogram
      • Rectangle
      • Rhombus
      • Square and their properties.
    8. Various theorems in Quadrilateral
      • Mid-Point theorem
      • Converse of Mid-Point theorem and Intercept theorem
    9. Similar Triangles
      • Similarity
      • Properties of Similar Polygons
      • Basic Propertionality theorem and its Converse
      • Vertical Angle bisector theorem and its Converse
    10. Criteria for Similarity of Triangles
      • SSS, SAS and AAA similarity
        1. Areas and Perimeters of Similar Triangles
        2. The ratios of similar Triangles and Perimeters of Similar Triangles
      • Right triangle and Pythagorean theorem
        1. Pythagorean theorem and its Converse
        2. Mean proportionality relations in Right triangle and conditions for verifying type of triangle
      • Right triangle-Trigonometry
        1. Different systems of measuring angles
        2. Trigonometric ratios
        3. T-ratios of (90 – x )
    11. Circles
      • Basic terms of Circle
      • Length of arc
      • Area of a sector
      • Circle theorems
      • Various theorems on Chord
      • Central angle theorem and its applications
      • Various theorems on Tangents
      • Perimeter and Area
      • Perimeter and Area of various triangles, quadrilaterals and Circles
        1. Volume and Surface area
        2. Volume and Surface area of Cuboid, cube, Cylinder, Cone and Sphere