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| − | <!-- This portal was created using subst:box portal skeleton -->
| + | = A Kite and its properties = |
| − | <!-- BANNER ACROSS TOP OF PAGE -->
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| − | {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
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| − | |style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
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| − | [http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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| − | |}
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| − | While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
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| − | | |
| − | = Concept Map =
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| − | [[File:kite.mm|flash]]</mm>
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| − | | |
| − | = Textbook =
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| − | To add textbook links, please follow these instructions to:
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| − | ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
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| − | | |
| − | =Additional Information=
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| − | ==Useful websites==
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| − | # http://www.transum.org/software/Fun_Maths/kite. This website has good description and activities about kites.
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| − | ==Reference Books==
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| − | | |
| − | = Teaching Outlines =
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| − | | |
| − | ==Concept # 1. A Kite and its properties==
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| | ===Learning objectives=== | | ===Learning objectives=== |
| | # A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent. | | # A kite is a quadrilateral with two distinct pairs of adjacent sides that are congruent. |
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| | # Compare kite with other quadrilaterals and make a list of similarities and differences between them. | | # Compare kite with other quadrilaterals and make a list of similarities and differences between them. |
| | | | |
| − | ===Activity No # ===
| + | [[Category:Quadrilaterals]] |
| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://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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| − | | |
| − | ==Concept #2. Measurements in a kite==
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| − | ===Learning objectives===
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| − | # A kite has two pairs of congruent sides.
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| − | # Its diagnols intersect at right angles.
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| − | # The sum of its four sides would be its perimetre.
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| − | # Its area is given by the formula <math>(1/2) (product of its diagnols)</math>
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| − | | |
| − | ===Notes for teachers===
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| − | ===Activity No # 1. Deriving formula for area of a kite===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | |}
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| − | *Estimated Time : 30 minutes.
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| − | *Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
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| − | *Prerequisites/Instructions, if any
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| − | # Basics of a triangle and kite should have been done.
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| − | *Multimedia resources: Laptop
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| − | *Website interactives/ links/ / Geogebra Applets
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| − | *Process:
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| − | # The teacher can project the geogebra file on kite.
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| − | # Show them that a kite is made of two isosceles traingles.
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| − | # Sum of areas of these two triangles would be the area of the kite.
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| − | *Developmental Questions
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| − | # What is a kite ?
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| − | # What are the properties of a kite.
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| − | # What other figures can you see in a kite ?
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| − | # What types of triangles are these ?
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| − | # Identify the two isosceles triangles ?
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| − | # What is the formula to find the area of a triangle ?
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| − | *Evaluation:
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| − | # Choosing which two traingles out of the 8 visible types would be easy to deduce the area of kite ?
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| − | *Question Corner:
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| − | # Recall the two formulae that you know to find the area of a triangle.
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| − | | |
| − | ===Activity No # ===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://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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| − | | |
| − | ==Concept # 3. Construction of a kite==
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| − | ===Learning objectives===
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| − | # Learn steps for constructing a kite with given measures.
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| − | ===Notes for teachers===
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| − | ===Activity No # 1. Construction of a kite. ===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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| − | |}
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| − | *Estimated Time : 20 minutes.
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| − | *Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
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| − | *Prerequisites/Instructions, if any:
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| − | # Students should have prior knowledge about a kite and its properties.
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| − | # They should know a perpendicular line and its construction.
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| − | # They should know to construct a line segment of given length by constructing arcs.
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| − | *Multimedia resources: Laptop
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| − | *Website interactives/ links/ / Geogebra Applets: This geogebra file has been done by ITfC-Edu-Team
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| − | <ggb_applet width="800" height="485" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
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| − | *Process:
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| − | # The teacher can initially have a recaptualation of the concept of a kite and its properties.
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| − | # Give them measures say, "Construct a kite which has its congruent sides as 4 cm and 6 cm a pair with one of its diagnols measuring 5cm.
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| − | # Can project the geogebra file and explain the steps of construction for the given measures.
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| − | * Draw a rough small kite labelling with the given measures.
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| − | * Begin with drawing a line segment, the diagnol of a given measure, here 5 cm. label it as AB.
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| − | * Draw a perpendicular bisector to this line segment AB.
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| − | * With A as centre construct an arc with 4cm as radius. Mark the intersecting point of arc with the perpendicular bisector as D. Join AD.
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| − | * With B as centre construct another arc with the same radius 4cm. You get the same point D as point of intersection .
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| − | * Join AD and BD which would measure 4cm each and would become one pair of congruent sides of the kite.
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| − | * Similarly draw arcs on the other side taking radius as 6cm to get other pair of congruent sides.
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| − | * ADBE would be the specified kite.
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| − | | |
| − | *Developmental Questions:
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| − | # What are the properties of a kite ?
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| − | # What measures are given for constructing a kite ?
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| − | # By which given measure can we begin the kite construction ?
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| − | # What is the angle between the two diagnols in a kite ?
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| − | # For what purpose are we drawing the perpendicular bisector ?
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| − | # What is the purpose of drawing an arc ?
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| − | # What should be measure of the radius of the arc ?
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| − | # Why should AD and BD be same ?
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| − | *Evaluation:
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| − | # Check if the constructed kite satisfies all of its properties.
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| − | *Question Corner:
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| − | # Can you think of any other method of kite construction for the given measures ?
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| − | | |
| − | ===Activity No # ===
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| − | {| style="height:10px; float:right; align:center;"
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| − | |<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;">
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| − | ''[http://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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| − | | |
| − | Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
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