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#1 2017-01-18 15:44:21
- Mathegocart
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Geometry: Consecutive sides that are congruent not a paralellogram?
If a quadrilateral has two consecutive sides that are congruent, shouldn't it be a parallelogram? Tinkering around with EM implies that it might be true, so could anyone give me a counterexample?
The integral of hope is reality.
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#2 2017-01-18 21:31:05
- Bob
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Re: Geometry: Consecutive sides that are congruent not a paralellogram?
Do you mean that one pair of adjacent sides are equal in length?? In that case there are lots of alternatives. It could be a kite; or an arrowhead; or just an anyquad. If you draw those two lines then you've fixed three out of four points. Then put the fourth point anywhere you want.
If that isn't the problem, please explain what you mean here by congruent. I would normally only use that term for a whole shape not just some lines.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2017-01-18 23:11:19
- Mathegocart
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Re: Geometry: Consecutive sides that are congruent not a paralellogram?
Never type questions at night, my question was "If two pairs of consecutive sides are congruent, then it is a parallelogram.". I wanted a specific counterexample, let me check my tinkering around for some..
The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.
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#4 2017-01-18 23:30:04
- bobbym
- bumpkin
- From: Bumpkinland
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Re: Geometry: Consecutive sides that are congruent not a paralellogram?
Does "congruent" mean equal and parallel?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2017-01-18 23:36:36
- Mathegocart
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Re: Geometry: Consecutive sides that are congruent not a paralellogram?
It only means equal.
The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.
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#6 2017-01-18 23:43:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Geometry: Consecutive sides that are congruent not a paralellogram?
That is a counterexample.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2017-01-18 23:44:30
- Bob
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Re: Geometry: Consecutive sides that are congruent not a paralellogram?
If a quadrilateral has one pair of sides that are equal in length and parallel then it is a parallelogram whatever the other sides are 'doing'.
Proof:
The sides cannot be adjacent as they are parallel so they must be opposite.
Let's suppose the quadrilateral is ABCD lettered in order around the shape and that AB = DC and AB // DC.
Join AC.
AC is a transversal so angle BAC = DCA .
In triangles ADC and CBA: AB = DC; BAC = DCA and AC is common to both. So these triangles are congruent (SAS).
So AD = BC and AD // BC.
So the other pair of sides are equal and parallel. That is the definition of a parallelogram.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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