Geometry

Triangles, Quadrilaterals, Circles, Coordinate Geometry and Basic Trigonometry

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Overview

Geometry forms a substantial portion of the Mathematics and Science paper in TS TET Paper II, testing both content knowledge and pedagogical understanding. This topic spans the entire upper primary mathematics curriculum (Classes 6-8) and connects visual reasoning with algebraic skills.

For TS TET, you must demonstrate mastery of properties, theorems and formulas across plane geometry (triangles, quadrilaterals, circles) and analytical geometry (coordinate geometry, basic trigonometry). Questions typically test application of properties, calculation of angles, lengths, areas and coordinates. Expect 8-12 questions from geometry content, plus pedagogy questions on teaching methods and common student misconceptions.

Success requires memorising key properties and theorems, practising numerical problems, and understanding how to teach these concepts using concrete materials and progressive abstraction.

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Key Concepts

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

• **Congruence and similarity**: Congruent triangles have identical shape and size (SSS, SAS, ASA, AAS, RHS criteria). Similar triangles have the same shape but different sizes — corresponding angles equal, sides proportional.

• **Quadrilateral hierarchy**: Quadrilaterals form a family — trapezium (one pair parallel sides) → parallelogram (both pairs parallel) → rectangle (all right angles) → square (all sides equal). Rhombus branches from parallelogram with all sides equal.

• **Circle terminology**: Radius, diameter, chord, arc, sector, segment, tangent, secant. A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.

• **Coordinate geometry fundamentals**: The Cartesian plane uses ordered pairs (x, y) to locate points. Distance and section formulas connect algebra with geometry.

• **Trigonometric ratios**: In a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. These ratios are constant for a given angle regardless of triangle size.

• **Pythagoras theorem**: In a right triangle, hypotenuse² = base² + perpendicular². This bridges geometry and algebra and appears repeatedly in coordinate geometry.

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Formulas / Key Facts

### Triangles