Triangles which are on the same base and in the same paralle

• astrololo
In summary, the conversation discusses a question about proposition 37 in Euclid's elements, specifically regarding the proof of a parallelogram. The question asks if having a figure with four sides and opposite sides parallel is enough to acknowledge the presence of parallelograms, and the response clarifies that this definition includes rectangles but is not limited to them. The conversation concludes by acknowledging a previous mistake in assuming a specific type of parallelogram.
astrololo
I have a small question regarding proposition 37 of the elements of Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI37.html

The only problem I got with the proof is the fact that we don't seem to prove that we do have parallelogram. We have a figure with 4 side and we know that each opposite sides are parallels to each other. Is this considered enough to acknowledge that we have parallelograms ?

Thank you!

astrololo said:
I have a small question regarding proposition 37 of the elements of Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI37.html

The only problem I got with the proof is the fact that we don't seem to prove that we do have parallelogram. We have a figure with 4 side and we know that each opposite sides are parallels to each other. Is this considered enough to acknowledge that we have parallelograms ?
That's how a parallelograph is defined.

Mark44 said:
That's how a parallelograph is defined.
But couldn't this be a rectangle ?

A rectangle is one type of parallelogram, one in which all four interior angles are equal.

Mark44 said:
A rectangle is one type of parallelogram, one in which all four interior angles are equal.
Ok, then he's not pointing to any specific case, just that we have a general parallelogram ? (That usually have 2 pairs of parallels) Is that how I'm supposed to understand it ? I did the mistake of assuming that we had a
Rhomboid

astrololo said:
Ok, then he's not pointing to any specific case, just that we have a general parallelogram ? (That usually have 2 pairs of parallels)
Fixed the above for you: "That usually always have 2 pairs of parallels"
astrololo said:
Is that how I'm supposed to understand it ? I did the mistake of assuming that we had a
Rhomboid

Mark44 said:
Fixed the above for you: "That usually always have 2 pairs of parallels"
thank you !

1. What does it mean for two triangles to be on the same base?

When two triangles are on the same base, it means that they share a common side, known as the base, and have different vertices on opposite ends of that base.

2. What is the significance of two triangles being on the same base?

The significance of two triangles being on the same base is that it allows us to easily compare and analyze their properties, such as their heights, areas, and angles.

3. Can two triangles on the same base have different heights?

Yes, two triangles on the same base can have different heights. This is because the height of a triangle is measured perpendicularly from the base to the opposite vertex, and the other sides of the triangles can have different lengths.

4. How does being in the same parallelogram affect the relationship between two triangles on the same base?

Being in the same parallelogram does not affect the relationship between two triangles on the same base. They will still share a common base and have different vertices on opposite ends, regardless of whether they are in the same parallelogram or not.

5. What is the formula for finding the area of two triangles on the same base?

The formula for finding the area of two triangles on the same base is: (1/2) x base x (height of one triangle + height of the other triangle). This formula takes into account the shared base as well as the different heights of the triangles.

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