Important Formulae: Geometry | Mathematics & Pedagogy Paper 1 for CTET & TET Exams - CTET & State TET PDF Download

Basic Geometrical Terms

• Point: Represented by a dot (.), denoted by a capital letter.
• Line Segment: A part of a line with two endpoints, named by its endpoints, e.g., AB.
• Line: Extends infinitely in both directions, no endpoints, named by any two points on it, e.g., line AB.
• Ray: A part of a line that starts at an endpoint and extends infinitely in one direction, named starting with the endpoint, e.g., ray AB (→).
• Plane: A flat surface extending infinitely in all directions, named using any three points on it, e.g., plane PQR.

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Types of Lines

• Parallel Lines: Lines on the same plane that never meet, symbol: || (e.g., XY || PQ).
• Intersecting Lines: Lines that cross each other at one point.
• Perpendicular Lines: Lines that intersect to form right angles (90°), symbol: ⊥ (e.g., AB ⊥ CD).

Measuring and Drawing Line Segments

• Measuring Length: Use a ruler; align the zero mark with one endpoint and read the length at the other endpoint.
• Drawing a Line Segment: Use a ruler to draw a line of specified length.

Angles

• Naming Angles:
  • Three-letter name: ∠PQR (vertex in the middle).
  • One-letter name: ∠Q (when there is only one angle at the vertex).
  • Using numbers: ∠1.
• Measuring Angles: Use a protractor; align the baseline with one arm of the angle and read the measure where the other arm intersects the scale.
• Types of Angles:
  • Acute: < 90°
  • Right: = 90°
  • Obtuse: > 90° and < 180°
  • Straight: = 180°
  • Reflex: > 180°

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Area

• Squares and Rectangles: Area = Length × Width
• Triangles: Area = (Base × Height) ÷ 2
• Circles: Area = πr² (where r is the radius)

Circle

• Parts of a Circle:
  • Centre: The midpoint, O.
  • Radius: A line segment from the centre to any point on the circle.
  • Chord: A line segment joining two points on the circle.
  • Diameter: A chord passing through the centre; Diameter = 2 × Radius.
  • Circumference: The boundary length of the circle.
• Interior and Exterior:
  • Points inside the circle are in the interior.
  • Points on the circle lie on the circle.
  • Points outside the circle are in the exterior.
• Drawing a Circle: Use a compass to draw a circle of a specified radius by fixing the compass at the centre and rotating it.

Tangrams

• Seven geometric shapes (five triangles, one square, and one parallelogram) used to create various forms and understand geometric concepts.