Difference between revisions of "Theorems and problems on parallelograms"
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<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"> | <div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"> | ||
''[http://karnatakaeducation.org.in/KOER/index.php/ಸಮನಾಂತರ_ಚತುರ್ಭಜದ_ಮೇಲಿನ_ಪ್ರಮೇಯಗಳು_ಹಾಗೂ_ಸಮಸ್ಯೆಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> | ''[http://karnatakaeducation.org.in/KOER/index.php/ಸಮನಾಂತರ_ಚತುರ್ಭಜದ_ಮೇಲಿನ_ಪ್ರಮೇಯಗಳು_ಹಾಗೂ_ಸಮಸ್ಯೆಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> | ||
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= Concept Map = | = Concept Map = | ||
__FORCETOC__ | __FORCETOC__ | ||
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=Additional Information= | =Additional Information= | ||
| + | # These videos provide proofs of theorems related to triangle and parallelogram on the same base and between same parallels | ||
| + | {{#widget:YouTube|id=Jc6GKk5lB5Y}} {{#widget:YouTube|id=AnMogR7Ih_g}} | ||
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| + | 2. Notes and solved problems (in Kannada) by Yakub Koyyur, GHS Nada, Belthangady Taluk, D.K. | ||
| + | |||
| + | [https://www.slideshare.net/secret/4sN3LIISyt4nmK ಸಮಾಂತರ ಚತುರ್ಭುಜಗಳು ಮತ್ತು ತ್ರಿಭುಜದ ವಿಸ್ತೀರ್ಣಗಳು] | ||
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==Useful websites== | ==Useful websites== | ||
| + | [http://www.homeschoolmath.net/teaching/g/area_3.php Exercises on area of parallelograms and triangles] | ||
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| + | [http://www.math-only-math.com/triangle-on-same-base-and-between-same-parallels.html Solved examples for triangles on same base and between parallels] | ||
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==Reference Books== | ==Reference Books== | ||
| + | NCERT mathematics- Chapter 9: [http://ncert.nic.in/textbook/pdf/iemh109.pdf#page=1&zoom=auto,-17,728 Areas of parallelograms and triangles] | ||
= Teaching Outlines = | = Teaching Outlines = | ||
| − | ==Concept #== | + | ==Concept #1. Area of parallelograms on same base and between same parallels== |
===Learning objectives=== | ===Learning objectives=== | ||
| + | 1. Parallelograms on the same base and between same parallels are equal in area. | ||
| + | |||
| + | 2. Area of a parallelogram is the product of its base and the corresponding altitude. | ||
| + | |||
| + | 3. Parallelograms on the same base and having equal area lie between same parallels. | ||
| + | |||
===Notes for teachers=== | ===Notes for teachers=== | ||
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.'' | ''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.'' | ||
===Activity No # === | ===Activity No # === | ||
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| + | ==Concept #2. Area of triangles on same base and between same parallels== | ||
| + | ===Learning objectives=== | ||
| + | 1. Triangles on same base and between same parallels have equal area. | ||
| + | |||
| + | 2s. Area of a triangle is half the product of its base and the corresponding altitude. | ||
| + | |||
| + | 3. Triangles on the same base and of equal area lie between the same parallels. | ||
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===Notes for teachers=== | ===Notes for teachers=== | ||
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===Activity No # === | ===Activity No # === | ||
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| + | ==Concept #2. Mid-point theorem== | ||
| + | ===Learning objectives=== | ||
| + | # The segment connecting mid-point of any two sides of a triangle is parallel to the third side | ||
| + | # The length of the segment connecting the mid-point of two sides is equal to half the third side. | ||
| + | |||
| + | ===Notes for teachers=== | ||
===Activity No # === | ===Activity No # === | ||
| − | + | [[Quadrilaterals-Activity-Mid-point_theorem]] | |
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= Hints for difficult problems = | = Hints for difficult problems = | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| − | |''' | + | |'''No''' |
|'''Explanation''' | |'''Explanation''' | ||
|''' Analysis''' | |''' Analysis''' | ||
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= Math Fun = | = Math Fun = | ||
| − | + | [[Category:Class 9]] | |
| − | + | [[Category:Quadrilaterals]] | |
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Latest revision as of 22:09, 4 November 2019
Concept Map
Textbook
Karnataka state textbook :Chapter 9
Additional Information
- These videos provide proofs of theorems related to triangle and parallelogram on the same base and between same parallels
2. Notes and solved problems (in Kannada) by Yakub Koyyur, GHS Nada, Belthangady Taluk, D.K.
ಸಮಾಂತರ ಚತುರ್ಭುಜಗಳು ಮತ್ತು ತ್ರಿಭುಜದ ವಿಸ್ತೀರ್ಣಗಳು
Useful websites
Exercises on area of parallelograms and triangles
Solved examples for triangles on same base and between parallels
Reference Books
NCERT mathematics- Chapter 9: Areas of parallelograms and triangles
Teaching Outlines
Concept #1. Area of parallelograms on same base and between same parallels
Learning objectives
1. Parallelograms on the same base and between same parallels are equal in area.
2. Area of a parallelogram is the product of its base and the corresponding altitude.
3. Parallelograms on the same base and having equal area lie between same parallels.
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activity No #
Concept #2. Area of triangles on same base and between same parallels
Learning objectives
1. Triangles on same base and between same parallels have equal area.
2s. Area of a triangle is half the product of its base and the corresponding altitude.
3. Triangles on the same base and of equal area lie between the same parallels.
Notes for teachers
Activity No #
Concept #2. Mid-point theorem
Learning objectives
- The segment connecting mid-point of any two sides of a triangle is parallel to the third side
- The length of the segment connecting the mid-point of two sides is equal to half the third side.
Notes for teachers
Activity No #
Quadrilaterals-Activity-Mid-point_theorem
Hints for difficult problems
Here is a micro analysis of solution for a problem [geometry_problemsolving.odt here]
| No | Explanation | Analysis | |||
| 1 | 
|
Drawing ABCD.Cyclic orderD above | |||
| 2 | AB=CD=4X | Propertiesof parallelogram | |||
| 3 | AD=BC=2X+1 | Propertiesof parallelogram | |||
| 4 | AD=BC=2X+1 | Propertiesof parallelogram | 5 | AD=BC=2X+1 | Propertiesof parallelogram |
| 6 | AD=BC=2X+1 | Propertiesof parallelogram | |||
| 7 | AD=BC=2X+1 | Propertiesof parallelogram | |||
| 8 | AD=BC=2X+1 | Propertiesof parallelogram |
|}