Geometry: Triangles, Quadrilaterals, Congruence and Similarity

Overview

Geometry forms a significant portion of the Mathematics section in CG TET Paper II, typically contributing 3–5 questions. This topic tests your understanding of shapes, their properties, and logical reasoning—skills essential for teaching upper primary students (Classes VI–VIII).

The scope covers two major plane figures (triangles and quadrilaterals) along with two fundamental concepts for comparing figures (congruence and similarity). Mastery here requires memorising properties and theorems, but more importantly, understanding *why* these properties hold and *how* to apply them in problem-solving.

For exam success, focus on: triangle classification and angle properties, quadrilateral properties (especially parallelograms), the five congruence criteria, and the distinction between congruence and similarity. These concepts also appear in EVS-integrated questions about measurement and spatial reasoning.

Key Concepts

• **Triangle Angle Sum Property**: The sum of interior angles of any triangle equals 180°. This is the foundation for solving most triangle problems.

• **Exterior Angle Theorem**: An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

• **Triangle Inequality**: The sum of any two sides of a triangle must be greater than the third side. This determines whether three given lengths can form a triangle.

• **Congruence means identical**: Two figures are congruent if they have exactly the same shape AND size—one can be superimposed on the other perfectly.

• **Similarity means same shape, different size**: Similar figures have equal corresponding angles and proportional corresponding sides. All congruent figures are similar, but not all similar figures are congruent.

• **Quadrilateral Angle Sum**: The sum of interior angles of any quadrilateral equals 360°.

• **Parallelogram Properties**: Opposite sides are equal and parallel; opposite angles are equal; diagonals bisect each other.

• **Special Quadrilaterals Hierarchy**: Square → Rectangle → Parallelogram → Quadrilateral (each inherits properties from the level above).

Formulas / Key Facts

**Triangle Formulas:**

• Sum of angles = 180°
• Exterior angle = Sum of two interior opposite angles
• Area = (1/2) × base × height
• Area using Heron's formula: √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2

**Quadrilateral Formulas:**