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Basic Geometry Question
April 24, 2020, 03:46 PM
parallelBasic Geometry Question
So... I've made a living from being a 3D modeler , a staff architect, and running my small drafting & design firm. Now I'll admit that, while I know enough math and geometry to do what I need to do, I'm certainly no math or geometry whiz.
With that said, here's the question; can a triangle be both an isosceles triangle AND an equilateral triangle at the same time?
A penny saved is a government oversight. April 24, 2020, 03:49 PM
a1abdjquote:
isosceles triangle AND an equilateral triangle at the same time?
Yes
April 24, 2020, 03:50 PM
WaterburyBobquote:
Originally posted by parallel:
So... I've made a living from being a 3D modeler , a staff architect, and running my small drafting & design firm. Now I'll admit that, while I know enough math and geometry to do what I need to do, I'm certainly no math or geometry whiz.
With that said, here's the question; can a triangle be both an isosceles triangle AND an equilateral triangle at the same time?
It depends on the definition that you use. One definition allows it.
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April 24, 2020, 03:50 PM
AeteoclesYes.
April 24, 2020, 03:50 PM
honestlouI'm certainly rusty, but I'm pretty certain the answer is "no". By definition an isosceles triangle has exactly two equal sides- no more, no less. An equilateral triangle has three equal sides.
April 24, 2020, 03:51 PM
Otto PilotDepends on your definition of isosceles. I seem to recall that some say it is "exactly" two equal sides, some say "at least", so equilateral would be a special subset of isosceles.
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April 24, 2020, 04:22 PM
c1steveWhat about a 60-60-60 triangle. Two sides would be equal, and all angles are equal.
-c1steve
April 24, 2020, 04:31 PM
DrDanquote:
Originally posted by c1steve:
What about a 60-60-60 triangle. Two sides would be equal, and all angles are equal.
A triangle with all equal angles necessarily has all equal sides, and hence is equilateral.
This space intentionally left blank. April 24, 2020, 04:39 PM
flashguyMy answer is "Yes". An equilateral triangle has 2 equal sides, so qualifies as isoceles, also--it is a special case. I have never seen a definition of isoceles triangle that would exclude an equilateral triangle from being one.
In a similar fashion, is a square a rectangle or a rhombus, and a rectangle a parallelogram? Yes, to all 3 questions--they are merely special cases.
flashguy
Texan by choice, not accident of birth April 24, 2020, 04:42 PM
stoic-oneI always understood an isosceles to be "at least 2 equal sides", so in theory, yes.
April 24, 2020, 04:49 PM
Skins2881quote:
Originally posted by DrDan:
quote:
Originally posted by c1steve:
What about a 60-60-60 triangle. Two sides would be equal, and all angles are equal.
A triangle with all equal angles necessarily has all equal sides, and hence is equilateral.
And also isosceles triangle as well.
Just as a square is a parallelogram as well as a rhombus and a rectangle.
Jesse
Sic Semper Tyrannis April 24, 2020, 04:56 PM
DrDanquote:
Originally posted by Skins2881:
quote:
Originally posted by DrDan:
quote:
Originally posted by c1steve:
What about a 60-60-60 triangle. Two sides would be equal, and all angles are equal.
A triangle with all equal angles necessarily has all equal sides, and hence is equilateral.
And also isosceles triangle as well.
Just as a square is a parallelogram as well as a rhombus and a rectangle.
Not disputing that, just pointing out that three equal angles is equivalent to three equal sides.
This space intentionally left blank. April 24, 2020, 07:43 PM
nhtagmemberyes
April 24, 2020, 08:01 PM
V-TailAll equilateral triangles are isosceles triangles.
Not all isosceles triangles are equilateral triangles.
הרחפת שלי מלאה בצלופחים April 24, 2020, 08:04 PM
Skins2881quote:
Originally posted by V-Tail:
All equilateral triangles are isosceles triangles.
Not all isosceles triangles are equilateral triangles.
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Jesse
Sic Semper Tyrannis