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Line 62: − = Concept 2 Axioms and postulates =+ − Line 75:
Line 74: − + − {| style="height:10px; float:right; align:center;"+ − |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">+ − ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>+ − + − Estimated Time+ − Materials/ Resources needed − Prerequisites/Instructions, if any − Multimedia resources − Website interactives/ links/ / Geogebra Applets − Process/ Developmental Questions − Evaluation − Question Corner − − ===Activity No # === − {| style="height:10px; float:right; align:center;" − |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> − ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − Estimated Time − Materials/ Resources needed − Prerequisites/Instructions, if any − Multimedia resources − Website interactives/ links/ / Geogebra Applets − Process/ Developmental Questions − Evaluation − Question Corner − − − − − The teacher can talk about Euclid and his contributions to geometry, Euclid's Elements (is a mathematical and geometric treatise consisting of 13 books written by the ancient Greek mathematician Euclid).<br> − Geometric basic facts taken for granted are called axioms. These are universally accepted and do not need any proofs. These statements are the basis to understand and prove higher geometrical theorems.<br> − − Euclid's Axioms (or Common Notions)<br> − *Axiom 1 - Things which equal the same thing also equal one another. − *Axiom 2 - If equals are added to equals, then the wholes are equal. − *Axiom 3 - If equals are subtracted from equals, then the remainders are equal. − *Axiom 4 - Things which coincide with one another equal one another. − *Axiom 5 - The whole is greater than the part. − − {| style="height:10px; float:right; align:center;" − |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> − ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − '''Estimated Time''':45 minutes<br> − '''Materials/ Resources needed'''<br> − Laptop, geogebra, projector and a pointer.<br> − '''*Prerequisites/Instructions, if any'''<br> − − '''Multimedia resources''' : Laptop<br> − '''Website interactives/ links/ / Geogebra Applets'''<br> − − − − <span> </span> − − <span></span><div id="ggbContainer11f623fdbe97ebe26092ac5e084b7458"></div><span></span> − − − ============= − − Process − Developmental Questions − − Evaluation − Ask students to give some more examples to reiterate the axioms.<br> − Question Corner − #What was the name of the book written by Euclid ? How many chapters did it have ? + + + + + + − ==Concept # 4. What is a theorem ? ==+ − ===Learning objectives=== − ===Notes for teachers=== − ===Activity No # === − {| style="height:10px; float:right; align:center;" − |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> − ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> − |} − Estimated Time − Materials/ Resources needed − Prerequisites/Instructions, if any − Multimedia resources − Website interactives/ links/ / Geogebra Applets − − <span> </span> − − − Process/ Developmental Questions − Evaluation − Question Corner − − = Hints for difficult problems = − − = Project Ideas = − − = Math Fun = − − '''Usage''' − − Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
Introduction to Euclid's Geometry (view source)
Revision as of 09:31, 24 April 2019
, 09:31, 24 April 2019no edit summary
#Certain statements which are valid in all branches of mathematics whose validity is taken for granted without seeking mathematical proofs is called axioms
#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.
#Some statement which are taken for granted in a particular branches of mathematics is called postulates.
==== Concept 2 - Axioms and postulates ====
====Concept 2 - Euclid's Axioms and Postulates====
*''First Axiom'': Things which are equal to the same thing are also equal to one another.
*''First Axiom'': Things which are equal to the same thing are also equal to one another.
*''Second Axiom'': If equals are added to equals, the whole are equal.
*''Second Axiom'': If equals are added to equals, the whole are equal.
*''Fifth Postulate'': That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side of which are the angles less than the two right angles.
*''Fifth Postulate'': That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side of which are the angles less than the two right angles.
=====Activities=====
=====Activities=====
===Activity No # ===
======[[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 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]]======
|}
=====Solved problems/ key questions (earlier was hints for problems).=====
#What was the name of the book written by Euclid ? How many chapters did it have ?
===Learning objectives===
===Notes for teachers===
===Activity No # 1. Euclid's Axiom #1===
============
#Given <P = <Q and <Q = <R, according to which axiom of Euclid, the relation between <P and <R is established ?
#Given <P = <Q and <Q = <R, according to which axiom of Euclid, the relation between <P and <R is established ?
#If a + b = 8cm, Is it true to say that a + b + y = 8 + y ?
#If a + b = 8cm, Is it true to say that a + b + y = 8 + y ?
#If AB = 4cm, CD = 8cm and PQ = two times AB. Are CD and PQ equal ? Which axiom is used for proving this ?
#If AB = 4cm, CD = 8cm and PQ = two times AB. Are CD and PQ equal ? Which axiom is used for proving this ?
===Projects (can include math lab/ science lab/ language lab)===
===Assessments - question banks, formative assessment activities and summative assessment activities===
=====Worksheets=====
======[file:///INTRODUCTION_TO_EUCLID_GEOMETRY.pdf Introduction to Euclid's geometry 1]======
======[file:///EUCLIDS_GEOMETRY.pdf Introduction to Euclid's geometry 2]======
Contributed by Rekha .D .R, Assistant Mistress, G.H.S , Jayanagar 9th Block, Bengaluru-69<span></span><span></span>
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