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| + | Investigating the diameter is the longest chord of a circle. |
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| − | = Concept Map = | + | ===Objectives=== |
| − | __FORCETOC__
| + | To understand longest chord passes through the centre and it is the diameter |
| − | <mm>[[circles_and_lines.mm|flash]]</mm>
| + | ===Estimated Time=== |
| | + | 30 minutes |
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| − | = Textbook = | + | ===Prerequisites/Instructions, prior preparations, if any=== |
| − | To add textbook links, please follow these instructions to:
| + | Prior knowledge of point, lines, angles, polygons |
| − | ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
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| − | =Additional Information= | + | ===Materials/ Resources needed=== |
| − | ==Useful websites== | + | * Digital : Computer, geogebra application, projector. |
| − | #[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants <br>
| + | * Non digital : Worksheet and pencil, compass, strings |
| − | #[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes<br>
| + | * Geogebra files : [https://ggbm.at/c4eg7q2u Diameter is longest chord.ggb] |
| − | #[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll] contains good simulations
| + | {{Geogebra|c4eg7q2u}} |
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| − | ==Reference Books== | + | ===Process (How to do the activity)=== |
| | + | Use the geogebra file to show how diameter is the longest chord. |
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| − | = Teaching Outlines
| + | Move the points on the circle to show the changes in the triangle. |
| − | Chord and its related theorems
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| − | ==Concept #1 CHORD==
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| − | ===Learning objectives===
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| − | The students should be able to:<br>
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| − | #Recall the meaning of circle and chord.<br>
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| − | #State Properties of chord.<br>
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| − | # By studying the theorems related to chords, the students should know that a chord in a circle is an important concept .
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| − | # They should be able to relate chord properties to find unknown measures in a circle.
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| − | # They should be able to apply chord properties for proof of further theorems in circles.
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| − | ===Notes for teachers===
| + | What is the condition with respect to sides for formation of a triangle. Sum of two sides is larger than the third side. |
| − | A chord is a straight line joining 2 points on the circumference of a circle. Chords within a circle can be related many ways. The theorems that involve chords of a circle are :
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| − | Perpendicular bisector of a chord passes through the center of a circle.
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| − | Congruent chords are equidistant from the center of a circle.
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| − | If two chords in a circle are congruent, then their intercepted arcs are congruent.
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| − | If two chords in a circle are congruent, then they determine two central angles that are congruent.
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| − | ===Activity No 1 Theorem 1: Perpendicular bisector of a chord passes through the center of a circle. ===
| + | Compare the chord length with sum of two radii. When is the triangle reduced to a line segment. |
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| − | *Estimated Time <br>
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| − | 20 minutes
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| − | *Materials/ Resources needed:
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| − | Laptop, Geogebra file, projector and a pointer.
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| − | *Prerequisites/Instructions, if any
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| − | # The students should know the basic concepts of a circle and its related terms.
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| − | # They should have prior knowledge of chord and construction of perpendicular bisector to the chord.
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| − | *Multimedia resources: Laptop
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| − | *Website interactives/ links/ / Geogebra Applets
| + | What can you conclude about the chord? When is it the largest? |
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| − | *Process:
| + | [[Category:Circles]] |
| − | # Show the children the geogebra file.
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| − | # Let them identify the chord. Ask them to define a chord.
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| − | # perpendicular bisector.
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| − | # Show them the 2nd chord.
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| − | # Let students observe if everytime the perpendicular bisector of the chord passes through the centre of the circle.
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| − | *Developmental Questions:
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| − | # What is a chord ?
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| − | # At how many points on the circumference does the chord touch a circle .
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| − | # What is a bisector ?
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| − | # What is a perpendicular bisector ?
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| − | # In each case the perpendicular bisector passes through which point ?
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| − | # Can anyone explain why does the perpendicular bisector always passes through the centre of the circle ?
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| − | *Evaluation
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| − | # What is the angle formed at the point of intersection of chord and radius ?
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| − | # Are the students able to understand what a perpendicular bisector is ?
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| − | # Are the students realising that perpendicular bisector drawn for any length of chords for any circle always passes through the center of the circle .
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| − | *Question Corner:
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| − | # What do you infer ?
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| − | # How can you reason that the perpendicular bisector for any length of chord always passes through the centre of the circle.
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| − | ===Activity No # ===
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | *Estimated Time
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| − | *Materials/ Resources needed
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| − | *Prerequisites/Instructions, if any
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| − | *Multimedia resources
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process/ Developmental Questions
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| − | *Evaluation
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| − | *Question Corner
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| − | ==Concept #2.SECANT==
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| − | ===Learning objectives===
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| − | ===Notes for teachers===
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| − | ===Activity No # ===
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | *Estimated Time
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| − | *Materials/ Resources needed
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| − | *Prerequisites/Instructions, if any
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| − | *Multimedia resources
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process/ Developmental Questions
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| − | *Evaluation
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| − | *Question Corner
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| − | ===Activity No # ===
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | *Estimated Time
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| − | *Materials/ Resources needed
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| − | *Prerequisites/Instructions, if any
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| − | *Multimedia resources
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process/ Developmental Questions
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| − | *Evaluation
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| − | *Question Corner
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| − | ==Concept #3.TANGENT==
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| − | ===Learning objectives===
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| − | ===Notes for teachers===
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| − | ===Activity No # ===
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | *Estimated Time
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| − | *Materials/ Resources needed
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| − | *Prerequisites/Instructions, if any
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| − | *Multimedia resources
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process/ Developmental Questions
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| − | *Evaluation
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| − | *Question Corner
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| − | | |
| − | ===Activity No # ===
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| − | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | |}
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| − | *Estimated Time
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| − | *Materials/ Resources needed
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| − | *Prerequisites/Instructions, if any
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| − | *Multimedia resources
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process/ Developmental Questions
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| − | *Evaluation
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| − | *Question Corner
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| − | = Hints for difficult problems =
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| − | = Project Ideas =
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| − | = Math Fun =
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| − | '''Usage'''
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