Show two parrallelograms have same area

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In summary, the conversation is about proving a proposition from Euclid, which states that AD and EF lie on a line parallel to BC. The goal is to show that the area of ABCD is equal to the area of BCFE. To do so, it is necessary to first prove that triangle ABE is congruent to triangle DCF and then show that triangle GBC is congruent to triangle GED. The speaker knows how to prove that the corresponding angles are equal, but needs help with showing that the corresponding sides are congruent, specifically AB = DC, AE = EF, and BE = CF. The other person provides a clue by mentioning that the lines are parallel and therefore the sides are almost trivially equal.
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DEMJR
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This is a proposition from Euclid that I want to prove (see attachment). AD and EF lie on a line parallel to BC. I want to show that Area of ABCD = Area of BCFE. I believe to prove this I must first show that triangle ABE is congruent to triangle DCF (then show that triangle GBC = triangle GED).

I know how to show that all the corresponding angles are the same for both triangles. I just do not know how to prove that the corresponding sides are congruent. Could you give me a clue on how to think about or begin showing that AB = DC or AE = EF or BE = CF? Thanks a bunch.
 

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Hi DEMJR! :smile:
DEMJR said:
… Could you give me a clue on how to think about or begin showing that AB = DC

But they're parallel lines cutting parallel lines (ie a parallelogram) …

they're almost trivially equal :wink:​
 

Related to Show two parrallelograms have same area

1. How do you show that two parallelograms have the same area?

To show that two parallelograms have the same area, you can use the formula A = bh where A is the area, b is the base, and h is the height. Measure the base and height of each parallelogram and plug the values into the formula. If the resulting values are the same for both parallelograms, then they have the same area.

2. Can two parallelograms with different shapes have the same area?

Yes, two parallelograms with different shapes can have the same area. As long as the base and height measurements result in the same value when plugged into the formula A = bh, the parallelograms will have the same area.

3. What is the difference between congruent and equal parallelograms?

Congruent parallelograms have the same shape and size, while equal parallelograms have the same area but may have different shapes. In other words, congruent parallelograms are identical, while equal parallelograms have the same amount of space inside but may look different.

4. Can you use the Pythagorean Theorem to show that two parallelograms have the same area?

No, the Pythagorean Theorem cannot be used to show that two parallelograms have the same area. This theorem is used to find the length of the sides of a right triangle, and does not apply to parallelograms.

5. Are there any other methods to show that two parallelograms have the same area?

Yes, there are other methods to show that two parallelograms have the same area. One method is to divide the parallelograms into smaller, congruent shapes (such as triangles or rectangles) and then compare the areas of these smaller shapes. Another method is to use the concept of scaling, where the lengths of the sides are multiplied by a factor to create two similar parallelograms with the same area.

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