Theorems and problems on parallelograms

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ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

Concept Map

Textbook

Karnataka state textbook :Chapter 9

Additional Information

  1. 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

  1. The segment connecting mid-point of any two sides of a triangle is parallel to the third side
  2. 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 Parall.png 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

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