# Theorems and problems on parallelograms

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# Textbook

1. These videos provide proofs of theorems related to triangle and parallelogram on the same base and between same 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.

## 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.

## 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.

# 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

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