USA - Geometry - Syllabus

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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