Equivalent Versions Of Euclid's Fifth Postulate
Chapter Name : Introduction To Euclid's Geometry |
Sub Topic Code : 104_09_05_03_01 |
Topic Name : Equivalent Versions Of Euclid's Fifth Postulate |
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Sub Topic Name : Equivalent Versions Of Euclid's Fifth Postulate |
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Introduction
The Play fair axiom is a version of the fifth postulate which says for a point outside a given line, there exists only one line that passes that point and is parallel to the given line.
Pre-Requisites:
Basic Geometric concepts, Parallel lines
Activity:
Place a straw and a cap not on it. Place other straws on the cap. Observe how there can be only one straw that can be placed on the cap and be parallel to the first straw.
Real Life Question:
Do equivalents help in cross checking assumptions and theories?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Geometry | Measuring size, shape and position. |
| Axiom | Universally true statement used throughout mathematics. |
| Postulate | Assumptions specific to geometry. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Straws and a cap | It can show the Play fair’s axiom diagrammatically. |
Real life uses :
In geometrical applications.
Practical examples around us
| Examples | Explainations |
|---|---|
| Parallel lines in flat surfaces | Shows the working of the fifth postulate. |
What you learn in Theory:
Playfair’s axiom - Equivalent version of Euclid’s Fifth Postulate.
What you learn in Practice:
The fifth postulate holds good only for flat surfaces.