Geometry and Trigonometry

Overview

Geometry and Trigonometry form the backbone of the Mathematics section in TN TET Paper II. This topic carries significant weightage, typically accounting for 8-12 questions across both content knowledge and pedagogical application. The scope covers triangles (properties, congruence, similarity), circles (theorems, tangents, chords), coordinate geometry (distance, section formula, straight lines), and basic trigonometry (ratios, identities, heights and distances).

For classes 6-8, students transition from intuitive geometry to formal proofs and from concrete shapes to abstract coordinate systems. As a TET aspirant, you must demonstrate both mathematical competence and awareness of how children develop geometric reasoning. Expect direct calculation problems, theorem applications, and questions linking geometry concepts to classroom teaching strategies.

Mastery here requires memorising key formulas, understanding theorem conditions, and recognising common problem patterns. This topic also connects strongly to mensuration, so clarity on basic properties will help across multiple areas.

Key Concepts

• **Triangle Classification**: By sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). The angle sum property states that interior angles always total 180°.

• **Congruence Criteria**: Two triangles are congruent if they satisfy SSS, SAS, ASA, AAS, or RHS (for right triangles). Congruent triangles have equal corresponding sides and angles.

• **Similarity Criteria**: Triangles are similar if corresponding angles are equal (AA criterion) or sides are proportional (SSS or SAS similarity). Similar triangles have proportional sides but not necessarily equal.

• **Circle Fundamentals**: A circle is the locus of points equidistant from a centre. Key parts include radius, diameter, chord, arc, sector, and segment. The diameter is the longest chord.

• **Circle Theorems**: Angle in a semicircle is 90°. Angles in the same segment are equal. The perpendicular from the centre bisects the chord. Tangent is perpendicular to the radius at the point of contact.

• **Coordinate Geometry Basics**: The Cartesian plane uses ordered pairs (x, y). The x-axis is horizontal, y-axis is vertical. Quadrants are numbered anticlockwise from the top-right.

• **Trigonometric Ratios**: For a right triangle with angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Reciprocals are cosec, sec, and cot.

• **Standard Angle Values**: Memorise values for 0°, 30°, 45°, 60°, and 90°. These appear repeatedly in calculations.