Proving triangles congruent with circles [closed]












1












$begingroup$


I have a proof that looks like the following, not really sure where to start/how to solve. Any help would be appreciated.



Given: circle $S$ and circle $T$ intersect at $M$ and $O$.
Prove: $triangle MST cong triangle OST$



enter image description here






geometry circle triangle







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$endgroup$



closed as off-topic by Brahadeesh, Paul Frost, Batominovski, Davide Giraudo, DRF Dec 11 '18 at 21:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Brahadeesh, Paul Frost, Davide Giraudo, DRF

If this question can be reworded to fit the rules in the help center, please edit the question.
















  • $begingroup$
    What methods of proving triangle congruence do you know?
    $endgroup$
    – Blue
    Jan 23 '14 at 22:20






  • 1




    $begingroup$
    There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
    $endgroup$
    – amWhy
    Jan 23 '14 at 22:21


















1












$begingroup$


I have a proof that looks like the following, not really sure where to start/how to solve. Any help would be appreciated.



Given: circle $S$ and circle $T$ intersect at $M$ and $O$.
Prove: $triangle MST cong triangle OST$



enter image description here






geometry circle triangle







share|cite|improve this question











$endgroup$



closed as off-topic by Brahadeesh, Paul Frost, Batominovski, Davide Giraudo, DRF Dec 11 '18 at 21:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Brahadeesh, Paul Frost, Davide Giraudo, DRF

If this question can be reworded to fit the rules in the help center, please edit the question.
















  • $begingroup$
    What methods of proving triangle congruence do you know?
    $endgroup$
    – Blue
    Jan 23 '14 at 22:20






  • 1




    $begingroup$
    There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
    $endgroup$
    – amWhy
    Jan 23 '14 at 22:21
















1












1








1





$begingroup$


I have a proof that looks like the following, not really sure where to start/how to solve. Any help would be appreciated.



Given: circle $S$ and circle $T$ intersect at $M$ and $O$.
Prove: $triangle MST cong triangle OST$



enter image description here






geometry circle triangle







share|cite|improve this question











$endgroup$




I have a proof that looks like the following, not really sure where to start/how to solve. Any help would be appreciated.



Given: circle $S$ and circle $T$ intersect at $M$ and $O$.
Prove: $triangle MST cong triangle OST$



enter image description here






geometry circle triangle




geometry circle triangle






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 23 '14 at 22:45









Constructor

1,044718




1,044718










asked Jan 23 '14 at 22:16









NovicodeNovicode

128116




128116




closed as off-topic by Brahadeesh, Paul Frost, Batominovski, Davide Giraudo, DRF Dec 11 '18 at 21:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Brahadeesh, Paul Frost, Davide Giraudo, DRF

If this question can be reworded to fit the rules in the help center, please edit the question.







closed as off-topic by Brahadeesh, Paul Frost, Batominovski, Davide Giraudo, DRF Dec 11 '18 at 21:54


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Brahadeesh, Paul Frost, Davide Giraudo, DRF

If this question can be reworded to fit the rules in the help center, please edit the question.












  • $begingroup$
    What methods of proving triangle congruence do you know?
    $endgroup$
    – Blue
    Jan 23 '14 at 22:20






  • 1




    $begingroup$
    There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
    $endgroup$
    – amWhy
    Jan 23 '14 at 22:21




















  • $begingroup$
    What methods of proving triangle congruence do you know?
    $endgroup$
    – Blue
    Jan 23 '14 at 22:20






  • 1




    $begingroup$
    There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
    $endgroup$
    – amWhy
    Jan 23 '14 at 22:21


















$begingroup$
What methods of proving triangle congruence do you know?
$endgroup$
– Blue
Jan 23 '14 at 22:20




$begingroup$
What methods of proving triangle congruence do you know?
$endgroup$
– Blue
Jan 23 '14 at 22:20




1




1




$begingroup$
There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
$endgroup$
– amWhy
Jan 23 '14 at 22:21






$begingroup$
There's no proof to verify! I've replaced the "proof verification" tag: use it when you have sketched out/written a proof and you want some "eyes" to look it over/check your work.
$endgroup$
– amWhy
Jan 23 '14 at 22:21












1 Answer
1






active

oldest

votes


















3












$begingroup$

First, note that the side ST is common to both triangles so you have a side in common.



Next, consider what you know about the lengths of SM and SO. What about the lengths of MT and TO? They both are the radius of the circles. Then you could use the Side-Side-Side to show congruence. Perhaps there is another way to use the angles here for an alternative but this seems rather straightforward if S and T are the center of each circle.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
    $endgroup$
    – Novicode
    Jan 23 '14 at 22:29










  • $begingroup$
    Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
    $endgroup$
    – JB King
    Jan 23 '14 at 22:31


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









3












$begingroup$

First, note that the side ST is common to both triangles so you have a side in common.



Next, consider what you know about the lengths of SM and SO. What about the lengths of MT and TO? They both are the radius of the circles. Then you could use the Side-Side-Side to show congruence. Perhaps there is another way to use the angles here for an alternative but this seems rather straightforward if S and T are the center of each circle.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
    $endgroup$
    – Novicode
    Jan 23 '14 at 22:29










  • $begingroup$
    Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
    $endgroup$
    – JB King
    Jan 23 '14 at 22:31
















3












$begingroup$

First, note that the side ST is common to both triangles so you have a side in common.



Next, consider what you know about the lengths of SM and SO. What about the lengths of MT and TO? They both are the radius of the circles. Then you could use the Side-Side-Side to show congruence. Perhaps there is another way to use the angles here for an alternative but this seems rather straightforward if S and T are the center of each circle.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
    $endgroup$
    – Novicode
    Jan 23 '14 at 22:29










  • $begingroup$
    Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
    $endgroup$
    – JB King
    Jan 23 '14 at 22:31














3












3








3





$begingroup$

First, note that the side ST is common to both triangles so you have a side in common.



Next, consider what you know about the lengths of SM and SO. What about the lengths of MT and TO? They both are the radius of the circles. Then you could use the Side-Side-Side to show congruence. Perhaps there is another way to use the angles here for an alternative but this seems rather straightforward if S and T are the center of each circle.






share|cite|improve this answer











$endgroup$



First, note that the side ST is common to both triangles so you have a side in common.



Next, consider what you know about the lengths of SM and SO. What about the lengths of MT and TO? They both are the radius of the circles. Then you could use the Side-Side-Side to show congruence. Perhaps there is another way to use the angles here for an alternative but this seems rather straightforward if S and T are the center of each circle.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Sep 6 '15 at 5:47









Community♦

1




1










answered Jan 23 '14 at 22:20









JB KingJB King

3,49911014




3,49911014












  • $begingroup$
    Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
    $endgroup$
    – Novicode
    Jan 23 '14 at 22:29










  • $begingroup$
    Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
    $endgroup$
    – JB King
    Jan 23 '14 at 22:31


















  • $begingroup$
    Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
    $endgroup$
    – Novicode
    Jan 23 '14 at 22:29










  • $begingroup$
    Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
    $endgroup$
    – JB King
    Jan 23 '14 at 22:31
















$begingroup$
Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
$endgroup$
– Novicode
Jan 23 '14 at 22:29




$begingroup$
Alright, I understand how you got SSS, and I was thinking about the same thing. ST is congruent to itself, so that's one side down. I know both SM and SO and congruent, and MT and TO are congruent, but I can't find what theorem proves it. It isn't definition of circle, is it?
$endgroup$
– Novicode
Jan 23 '14 at 22:29












$begingroup$
Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
$endgroup$
– JB King
Jan 23 '14 at 22:31




$begingroup$
Yes, it is the definition of circle that the curve is the set of points that are an equal distance from a center.
$endgroup$
– JB King
Jan 23 '14 at 22:31



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