Name: Euclid’s Fifth Postulate and the Equivalent
Uploaded: 2019-07-19
Duration: 8 min 53 s
Description: In this video, let's learn about Euclid’s Fifth Postulate and its significance. We will also learn about PLAYFAIR’S AXIOM, which is an equivalent form of the...

Question

How would you rewrite Euclid's fifth postulate so that it would be easier to understand?

Accepted Answer

Two lines are said to be parallel if they are equidistant from one other, and they do not have any point of intersection. In order to understand it easily let us take any line $l$ and a point $P$ not on $l .$

By Play fair’s axiom (equivalent to the fifth postulate), we know that there is a unique line $m$ through $P$ which is parallel to $l .$

Now, the distance of a point from a line is the length of the perpendicular from the point to the line.

Let $A B$ be the distance of any point on $m$ from $l$ and $C D$ be the distance of any point on $l$ from $m .$

We can observe that $A B = C D .$ In this way the distance will be the same for any point on $m$ to $l$ and any point on $l$ to $m$ .

So, parallel lines are always the same distance apart.

Mizoram Board Solutions for Chapter: Introduction to Euclid's Geometry, Exercise 2: EXERCISE

Mizoram Board Mathematics Solutions for Exercise - Mizoram Board Solutions for Chapter: Introduction to Euclid's Geometry, Exercise 2: EXERCISE

Questions from Mizoram Board Solutions for Chapter: Introduction to Euclid's Geometry, Exercise 2: EXERCISE with Hints & Solutions

Learn and Prepare for any exam you want !