triangle definition vs quadrilateral definition
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Consider a reflex quadrilateral ie one that has one internal angle > 180 degrees. Modify the quadrilateral so that the angle decreases. When the angle is less than 180 the shape is still a quadrilateral. When the angle is exactly 180 the shape is a triangle but is it still a quadrilateral, If not what definition of a quadrilateral has it violated? My wondering about this stems from a lecturer casually mentioning that "hour glass" quadrilateral where the corners are joined in the wrong order still counted and whether that inclusion extended to ones with an internal angle of 180.
geometry
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
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add a comment |
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Consider a reflex quadrilateral ie one that has one internal angle > 180 degrees. Modify the quadrilateral so that the angle decreases. When the angle is less than 180 the shape is still a quadrilateral. When the angle is exactly 180 the shape is a triangle but is it still a quadrilateral, If not what definition of a quadrilateral has it violated? My wondering about this stems from a lecturer casually mentioning that "hour glass" quadrilateral where the corners are joined in the wrong order still counted and whether that inclusion extended to ones with an internal angle of 180.
geometry
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
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If it has four vertices, it's a quadrilateral.
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– Vasya
Nov 27 '18 at 15:10
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"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
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– David K
Nov 27 '18 at 15:23
add a comment |
$begingroup$
Consider a reflex quadrilateral ie one that has one internal angle > 180 degrees. Modify the quadrilateral so that the angle decreases. When the angle is less than 180 the shape is still a quadrilateral. When the angle is exactly 180 the shape is a triangle but is it still a quadrilateral, If not what definition of a quadrilateral has it violated? My wondering about this stems from a lecturer casually mentioning that "hour glass" quadrilateral where the corners are joined in the wrong order still counted and whether that inclusion extended to ones with an internal angle of 180.
geometry
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
$endgroup$
Consider a reflex quadrilateral ie one that has one internal angle > 180 degrees. Modify the quadrilateral so that the angle decreases. When the angle is less than 180 the shape is still a quadrilateral. When the angle is exactly 180 the shape is a triangle but is it still a quadrilateral, If not what definition of a quadrilateral has it violated? My wondering about this stems from a lecturer casually mentioning that "hour glass" quadrilateral where the corners are joined in the wrong order still counted and whether that inclusion extended to ones with an internal angle of 180.
geometry
geometry
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
asked Nov 27 '18 at 14:35
Antony CornellAntony Cornell
111
111
$begingroup$
If it has four vertices, it's a quadrilateral.
$endgroup$
– Vasya
Nov 27 '18 at 15:10
$begingroup$
"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
$endgroup$
– David K
Nov 27 '18 at 15:23
add a comment |
$begingroup$
If it has four vertices, it's a quadrilateral.
$endgroup$
– Vasya
Nov 27 '18 at 15:10
$begingroup$
"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
$endgroup$
– David K
Nov 27 '18 at 15:23
$begingroup$
If it has four vertices, it's a quadrilateral.
$endgroup$
– Vasya
Nov 27 '18 at 15:10
$begingroup$
If it has four vertices, it's a quadrilateral.
$endgroup$
– Vasya
Nov 27 '18 at 15:10
$begingroup$
"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
$endgroup$
– David K
Nov 27 '18 at 15:23
$begingroup$
"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
$endgroup$
– David K
Nov 27 '18 at 15:23
add a comment |
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$begingroup$
If it has four vertices, it's a quadrilateral.
$endgroup$
– Vasya
Nov 27 '18 at 15:10
$begingroup$
"the shape is a triangle but is it still a quadrilateral ... ." I would say the shape is then concurrent with a triangle. It's only a triangle if you decide to delete a vertex.
$endgroup$
– David K
Nov 27 '18 at 15:23