EUCLID GEOMETRY (LECTURE 2)

LESSON 2    EUCLID GEOMETRY

DEAR STUDENTS

WELCOME TO THE CLASS!!

FEW REMINDERS:

The text in Red, is to be written in your register

·         The text in blue is to be viewed by clicking on it

Yesterdays learning outcomes 
1. Recall   Euclid's  axioms and its application      

                                                                                                             

1.     Take your  Mathematics Register

2.      Our handwriting reflects a lot about us. It will be awesome if you use good presentation and cursive hand writing

3.      Make a column on the right hand side, if you need to do any rough work

4.      Leave two lines where you finished yesterday’s work and draw a horizontal line

5.      Write today's date on the line after that.

6.      Pending Queries from yesterday (if any).......

7.      Please write the learning outcomes as mentioned below

Today's learning outcomes are  

I will be able to:
1. recall, THE POSTULATES

2.recall  , PLAYFAIR AXIOM

What are Axioms or Postulates ? (To  be written)

Axioms or Postulates are assumptions which are obvious universal truths. They are not proved
Euclid axioms are the assumptions which are used throughout mathematics while Euclid Postulates are the assumptions which are specific to geometry

click on the link for 4  POSTULATES

1. A straight line may be drawn from one point to another point. As per this postulate,there exists a unique line joining two points
   
2. A terminated line can be produced indefinitely. A terminated line or line segment is the segment of line joined by two separate point. As per this postulate, a line segment can be extended in in both direction to make a line
   
3. A circle can be drawn with any centre and any radius. As per this postulate, we can draw circles with any centre and any radius. For example,we can draw a circle on line segment with centre at its end point and radius as the length of the line segments
   
4. All right angles are equal to one another
   . A right angle is angle measuring ${90}^0$. As per this postulate ,all the right angles are equal and if we place one right angle over top of another right angle, they will coincide
   

click on the link  👇 to know                                                                                                                5th postulate and Playfair Axiom

5.. if two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the straight lines if produced indefinitely meet on that side on which the angles are less than the two right angles
For Example 

Here the line  PQ in below figure falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than ${180}^0$ on the left side of  PQ. Therefore, the lines AB and CD will eventually intersect on the left side of  PQ.

Play fair Axiom
This is equivalent version of Euclid fifth law which states lines will not intersect when the angle is equal two right angle
For every line l and for every point P not lying on the line l, there exists a unique line m passing through P and Parallel to l


.
lets TEST  ourself by completing the given crossword
Crossword for Euclid Geometry

Across

1. He was the student of Thales.
8. The terms specifically used for assumption in Geometry.
9. A _______ is a theorem that is usually considered an "easy consequence" of another theorem.
Down

2. Square and circular ____ were used for household rituals.
3. The instrument consists of nine interwoven isosceles triangles
4. Euclid was a teacher of mathematics in Alexandria in _______
5. Thales belongs to ______
6. They are the statements which are proved
7. The term used for the assumptions which are used throughout mathematics
1. Pythagoras
2. altars
3. sriyantra
4. Egypt
5. Greece
6. Theorem
7. axiom
8. postulate
9. Corollary
Don't worry if you couldn't attempt all. Answers are given .


Exercise 5.2 (To be done in register) HW 

ALSO THE SOLVED EXAMPLES 


1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Solution:
Euclid’s fifth postulate: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
i.e., the Euclid’s fifth postulate is about parallel lines.
Parallel lines are the lines which do not intersect each other ever and are always at a constant perpendicular distance apart from each other. Parallel lines can be two or more lines.
A: If X does not lie on the line A then we can draw a line through X which will be parallel to that of the line A.
B: There can be only one line that can be drawn through the point X which is parallel to the line A.
Q2. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Solution:
Yes, Euclid’s fifth postulate does imply the existence of the parallel lines.
If the sum of the interior angles are equal to the sum of the right angles, then the two lines will not meet each other at any given point, hence making them parallel to each other.

∠1+∠3=180o
Or  ∠3+∠4=180o


NOW ITS QUIZ TIME 



Quiz Time

Question 1 It is known that if $x+z=100$ then $x+y+z=100+y$. The Euclid's axiom that illustrates this statement is ?
 A. Ist
 B. IInd
 C. IIIrd
 D. IVth
Question 2 Which of these is false
 A. Things equal to the same thing are equal
 B. Postulates are assumptions specific to geometry.
 C. A point has no dimension
 D. The statements that are proved are called axioms.
Question 3 Boundaries of solids are
 A. Surfaces
 B. curve
 C. line
 D. points
Question 4 Euclid divided his famous treatise "The Elements" into :
 A. 9 chapters
 B. 23 chapters
 C. 10 chapters
 D. 13 chapters
Question 5 The things which are double of the same thing are
 A. half of others
 B. double
 C. equals
 D. none of the above
Question 6 Euclid stated that all right angles are equal to each other in the form of ?
 A. Axiom
 B. definition
 Y C. theorem
 D. postulate
Answers    ....B,D,C,D,C,D
Cross word

Answers
1. Pythagoras
2. altars
3. sriyantra
4. Egypt
5. Greece
6. Theorem
7. axiom
8. postulate
9. Corollary
THATS ALL FOR THE DAY .  HAVE A GOOD DAY AND BE SAFE ☺