Geometry Basics – Madhya Pradesh TET (Teacher Eligibility)
(Quantitative Aptitude – Geometry)
Goal: Master the foundational concepts, formulas, and quick‑solve techniques that are repeatedly tested in the TET exam.
1. Simple Explanation
Geometry is the branch of mathematics that deals with shapes, their sizes, relative positions, and properties of space. In the TET exam, you’ll encounter questions on:
- Basic elements – points, lines, planes.
- Angles – types, relationships (complementary, supplementary).
- Triangles & Quadrilaterals – classification, properties, area, perimeter.
- Circles – radius, diameter, chord, arc, sector, tangent, secant.
- Coordinate Geometry – distance, midpoint, slope, equation of a line.
These topics form the core of quantitative aptitude for teachers and appear in a mix of multiple‑choice and short‑answer formats.
2. Key Points
2.1 Points, Lines & Planes
| Concept | Definition | Notes |
|---|---|---|
| Point | A location with no dimensions. | Usually denoted by a single letter (A, B, C). |
| Line | Infinite set of points extending in two directions. | Two points determine a line. |
| Plane | Flat, two‑dimensional surface extending infinitely. | Three non‑collinear points determine a plane. |
2.2 Angles
| Type | Symbol | Definition | Key Fact |
|---|---|---|---|
| Acute | < 90° | ||
| Right | 90° | ||
| Obtuse | > 90° & < 180° | ||
| Straight | 180° | ||
| Complementary | Two angles that add up to 90° | ||
| Supplementary | Two angles that add up to 180° |
2.3 Triangles
| Type | Criteria | Key Properties |
|---|---|---|
| Equilateral | All sides equal | All angles 60° |
| Isosceles | Two sides equal | Base angles equal |
| Scalene | No equal sides | |
| Right | One right angle | Pythagoras: (a^2 + b^2 = c^2) |
| Obtuse | One obtuse angle | |
| Acute | All angles < 90° |
Area Formulas
| Condition | Formula |
|---|---|
| General | (\displaystyle \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}) |
| Heron’s (sides a,b,c) | (\displaystyle \sqrt{s(s-a)(s-b)(s-c)}), where (s = \frac{a+b+c}{2}) |
| Right Triangle | (\displaystyle \frac{1}{2}ab) (legs as base & height) |
| With Circumradius (R) | (\displaystyle \text{Area} = abc/(4R)) |
Perimeter – sum of all side lengths.
2.4 Quadrilaterals
| Shape | Special Properties | Area Formula |
|---|---|---|
| Parallelogram | Opposite sides parallel & equal | (\displaystyle \text{Area} = \text{base} \times \text{height}) |
| Rectangle | Opposite sides equal, all angles 90° | (\displaystyle \text{Area} = \text{length} \times \text{breadth}) |
| Square | All sides equal, all angles 90° | (\displaystyle |