- #1
forevergone
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Vector Proofs: A Quadrilateral thing #2!
Thanks lightgrav!
Thanks lightgrav!
Last edited:
In summary: You can use the parallelogram law to get the result. In summary, Vector Proofs: A Quadrilateral thing #2! Thanks to lightgrav for providing a summary of the content.
- #2
celticsthree4
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forevergone said:
We had that problem on a geometry test in 9th grade, I will try digging it up and show you how
...if I can find it of course - #3
forevergone
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Any help is always appreciated!
- #4
lightgrav
Homework Helper
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you're given that dz = zb and az = zc , as your starting point.
What sums and differences of these equations show what you want?
What sums and differences of these equations show what you want?
- #5
forevergone
- 49
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az + zb = ab
cz + zd = cd
but az = zb, cz = cd therefore ab = cd!
Bah! That took like 5 minutes to see when I was spending 5 hours worth of time on it.
Thanks!
cz + zd = cd
but az = zb, cz = cd therefore ab = cd!
Bah! That took like 5 minutes to see when I was spending 5 hours worth of time on it.
Thanks!
- #6
lightgrav
Homework Helper
- 1,249
- 30
The key to this stuff is writing in symbols
JUST WHAT they tell you in words.
That's why everybody calls these things "Word Problems"!
JUST WHAT they tell you in words.
That's why everybody calls these things "Word Problems"!
- #7
forevergone
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But a new problem arises :\.
- #8
Diane_
Homework Helper
- 393
- 1
One way to do this is to show that you have a pair of congruent triangles. (There are actually several pair, but you only need one.) Remember the definition of a parallelogram - that'll give you the angles. There's one more property of parallelograms that will give you the sides that you need.
- #9
forevergone
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Diane_ said:
I need to do this through vector proofs, though. If I could use congruent triangles, I would've been long done this problem :).
- #10
daniel_i_l
Gold Member
- 868
- 0
You just have to show that 1/2(dc+da) = 1/2db. that means that the middle of db touches the middle of ac. This is easy to prove. Start with the two equations:
db = da + ab
db = dc + cb
and try to solve for 1/2(dc+da) in terms of db.
db = da + ab
db = dc + cb
and try to solve for 1/2(dc+da) in terms of db.
FAQ: Vector Proofs: A Quadrilateral thing
What is a vector proof?
A vector proof is a method of proving geometric theorems using the concept of vectors. It involves proving that two vectors are equal or parallel in order to show that certain geometric properties hold true.
How do you use vector proofs to prove properties of quadrilaterals?
To use vector proofs to prove properties of quadrilaterals, you need to define the vectors that represent the sides and diagonals of the quadrilateral. Then, you can use properties of vector operations such as addition, subtraction, and dot product to show that the sides and diagonals have certain relationships, which in turn prove the properties of the quadrilateral.
What are some common properties that can be proved using vector proofs for quadrilaterals?
Some common properties that can be proved using vector proofs for quadrilaterals include parallel sides, congruent sides, diagonals bisecting each other, and the diagonal lengths being equal.
Can vector proofs be used for other types of shapes besides quadrilaterals?
Yes, vector proofs can be used for other types of shapes as well, such as triangles, circles, and polygons. The key is to define the appropriate vectors for the given shape and use vector operations to prove the desired properties.
Are there any limitations to using vector proofs for geometric theorems?
While vector proofs can be a useful tool for proving geometric theorems, they do have some limitations. One limitation is that they require a strong understanding of vector operations and properties. Additionally, vector proofs may not be applicable to all types of geometric problems and may not be the most efficient method for every situation.