# 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.
• Trapezium
• Parallelogram
• Rectangle
• Rhombus
• Square and their properties.
• 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