Difference between revisions of "Axioms, Postulates And Theorems"
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# Some statement which are taken for granted in a particular branches of mathematics is called postulates. | # Some statement which are taken for granted in a particular branches of mathematics is called postulates. | ||
| − | + | ==== Concept 2 - Euclid' Axioms ==== | |
===== Activities ===== | ===== Activities ===== | ||
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====== [[Axiom 1: Things which are equal to the same thing are equal to one another|Things which are equal to the same thing are equal to one another]] ====== | ====== [[Axiom 1: Things which are equal to the same thing are equal to one another|Things which are equal to the same thing are equal to one another]] ====== | ||
| − | ==== '''[[Axiom 2 and 3: If equals are added or subtracted to equals, the wholes are equal|If equals are added or subtracted to equals, the wholes are equal]]''' ==== | + | ====== '''[[Axiom 2 and 3: If equals are added or subtracted to equals, the wholes are equal|If equals are added or subtracted to equals, the wholes are equal]]''' ====== |
| − | '''[[Axiom 4: Things which coincide with one another are equal to one another|Things which coincide with one another are equal to one another]]''' | + | |
| + | ====== '''[[Axiom 4: Things which coincide with one another are equal to one another|Things which coincide with one another are equal to one another]]''' ====== | ||
====== [[Axiom 5: The whole is greater than the part|The whole is greater than the part]] ====== | ====== [[Axiom 5: The whole is greater than the part|The whole is greater than the part]] ====== | ||
| + | [[Introduction to angles]] | ||
| − | + | Introduction to pairs of angles | |
| − | |||
| − | |||
| − | + | Solved problems | |
| − | + | Concept 3 - Points, lines and angles | |
===== Activities ===== | ===== Activities ===== | ||
Revision as of 13:32, 24 April 2019
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Concept Map
Additional resources
OER
Non-OER
- Web resources
- Video on angles - http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html
- Additional information on axioms and postulates
- To learn types of angles click here
- The following videos provide an introduction to axioms, postulates and lines
- Books and journals
- Textbooks:
- Syllabus documents (CBSE, ICSE, IGCSE etc)
Learning Objectives
Teaching Outlines
Concept 1 - Introduction to geometry
It is useful to discuss with students about Euclid and his great contribution to Mathematics. The below two statements helps to understand and prove the theorems in geometry. Also, through a combination of activities, help the students understand results in the nature of axioms and postulates.
- Certain statements which are valid in all branches of mathematics whose validity is taken for granted without seeking mathematical proofs is called axioms
- Some statement which are taken for granted in a particular branches of mathematics is called postulates.
Concept 2 - Euclid' Axioms
Activities
Things which are equal to the same thing are equal to one another
If equals are added or subtracted to equals, the wholes are equal
Things which coincide with one another are equal to one another
The whole is greater than the part
Introduction to pairs of angles
Solved problems
Concept 3 - Points, lines and angles