Mixing
Two sides of a triangle have equal length if the angles opposite them are equal. Is this true? If so, what is...
0
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I am told that two sides of a triangle have equal length if the angles opposite them are equal.
Is this true? If so, I would appreciate it if someone could tell me what the theorem called.
Thank you.
geometry
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
$endgroup$
add a comment |
0
$begingroup$
I am told that two sides of a triangle have equal length if the angles opposite them are equal.
Is this true? If so, I would appreciate it if someone could tell me what the theorem called.
Thank you.
geometry
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
$endgroup$
1
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
2
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
1
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
1
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30
add a comment |
0
0
0
$begingroup$
I am told that two sides of a triangle have equal length if the angles opposite them are equal.
Is this true? If so, I would appreciate it if someone could tell me what the theorem called.
Thank you.
geometry
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
$endgroup$
I am told that two sides of a triangle have equal length if the angles opposite them are equal.
Is this true? If so, I would appreciate it if someone could tell me what the theorem called.
Thank you.
geometry
geometry
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
asked Nov 24 '16 at 4:23
The PointerThe Pointer
2,64421638
2,64421638
1
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
2
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
1
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
1
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30
add a comment |
1
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
2
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
1
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
1
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30
1
1
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
2
2
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
1
1
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
1
1
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30
add a comment |
2 Answers
2
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oldest
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1
$begingroup$
It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)mapsto(B,A,C)$, hence $|AC|=|BC|$.
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
0
$begingroup$
It is called "sides opposite equal angles".
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
$endgroup$
add a comment |
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2 Answers
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2 Answers
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1
$begingroup$
It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)mapsto(B,A,C)$, hence $|AC|=|BC|$.
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
1
$begingroup$
It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)mapsto(B,A,C)$, hence $|AC|=|BC|$.
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
1
1
1
$begingroup$
It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)mapsto(B,A,C)$, hence $|AC|=|BC|$.
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
$endgroup$
It's an immediate consequence of the ASA congruence theorem (or axiom?): A triangle with equal angles at $A$ and $B$ is congruent to itself under $(A,B,C)mapsto(B,A,C)$, hence $|AC|=|BC|$.
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
answered Nov 24 '16 at 15:43
Christian BlatterChristian Blatter
175k8115327
175k8115327
add a comment |
add a comment |
0
$begingroup$
It is called "sides opposite equal angles".
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
$endgroup$
add a comment |
0
$begingroup$
It is called "sides opposite equal angles".
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
$endgroup$
add a comment |
0
0
0
$begingroup$
It is called "sides opposite equal angles".
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
$endgroup$
It is called "sides opposite equal angles".
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
answered Nov 24 '16 at 15:13
MickMick
11.9k21641
11.9k21641
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1
$begingroup$
It defines an isosceles triangle
$endgroup$
– imranfat
Nov 24 '16 at 4:24
$begingroup$
@imranfat I see. Is there a name for this theorem?
$endgroup$
– The Pointer
Nov 24 '16 at 4:25
2
$begingroup$
That's the converse of Proposition 5 of Book 1 in Euclid's Elements. Lookup 'pons asinorum`.
$endgroup$
– dxiv
Nov 24 '16 at 4:25
1
$begingroup$
@dxiv Got it. Thank you.
$endgroup$
– The Pointer
Nov 24 '16 at 4:26
1
$begingroup$
It isn't really named per se. People didn't really name things back then. Euclid just compiled 90% of the knowledge of the geometry he knew from Egypt and other places around Greece. The only thing truly 100% credible to him was the idea of the postulates and his proofs using them. He may have made a few propositions of his own, but I imagine the first 7 or 8 were already known to people. Just pointing that out.
$endgroup$
– The Great Duck
Nov 24 '16 at 4:30