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Prove all right angles are congruent?
up vote
3
down vote
favorite
Prove all right angles are congruent.
I only have to prove one side to this argument, so I just need to the the other argument.
So basically, if two angles are right, then they must be congruent is what I am trying to prove.
All I have is my assumption that the two angles are right. And conclusion, therefore the angles are congruent.
geometry euclidean-geometry noneuclidean-geometry
asked Mar 31 '15 at 23:50
user217443
2913
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
|
show 2 more comments
up vote
3
down vote
favorite
Prove all right angles are congruent.
I only have to prove one side to this argument, so I just need to the the other argument.
So basically, if two angles are right, then they must be congruent is what I am trying to prove.
All I have is my assumption that the two angles are right. And conclusion, therefore the angles are congruent.
geometry euclidean-geometry noneuclidean-geometry
asked Mar 31 '15 at 23:50
user217443
2913
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
1
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
1
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
Don't have that yet
– user217443
Apr 1 '15 at 0:26
10
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26
|
show 2 more comments
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Prove all right angles are congruent.
I only have to prove one side to this argument, so I just need to the the other argument.
So basically, if two angles are right, then they must be congruent is what I am trying to prove.
All I have is my assumption that the two angles are right. And conclusion, therefore the angles are congruent.
geometry euclidean-geometry noneuclidean-geometry
asked Mar 31 '15 at 23:50
user217443
2913
Prove all right angles are congruent.
I only have to prove one side to this argument, so I just need to the the other argument.
So basically, if two angles are right, then they must be congruent is what I am trying to prove.
All I have is my assumption that the two angles are right. And conclusion, therefore the angles are congruent.
geometry euclidean-geometry noneuclidean-geometry
geometry euclidean-geometry noneuclidean-geometry
asked Mar 31 '15 at 23:50
user217443
2913
asked Mar 31 '15 at 23:50
user217443
2913
asked Mar 31 '15 at 23:50
user217443
2913
asked Mar 31 '15 at 23:50
user217443
2913
asked Mar 31 '15 at 23:50
user217443
2913
2913
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
bumped to the homepage by Community♦ 2 days ago
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
1
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
1
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
Don't have that yet
– user217443
Apr 1 '15 at 0:26
10
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26
|
show 2 more comments
1
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
1
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
Don't have that yet
– user217443
Apr 1 '15 at 0:26
10
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26
1
1
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
1
1
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
Don't have that yet
– user217443
Apr 1 '15 at 0:26
Don't have that yet
– user217443
Apr 1 '15 at 0:26
10
10
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26
|
show 2 more comments
4 Answers
4
active
oldest
votes
up vote
0
down vote
We say that the angle $measuredangle AOB$ is the supplement of the angle $measuredangle Y$ if the latter is congruent to an adjacent angle $measuredangle BOC$ to $measuredangle AOB$ such that the points $A$, $O$ and $C$ are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements (by definition), you can prove that all right angles are congruent as follows:
Let $measuredangle AOB$ be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let $measuredangle BOC$ be an adjacent supplement of $measuredangle AOB$, then $measuredangle AOB cong measuredangle BOC$ and $A$, $0$, $C$ are colineal.
Now let $Y$ be any other right angle and consider $D$ an exterior point of $measuredangle AOB$ such that $measuredangle AOD$ is a right angle congruent to $Y$. Here you have to prove that: $B$, $O$ and $D$ are colineal and once you have this prove that $measuredangle AOBcong measuredangle AOD$ (using "vertex opposites" arguments), I'm leaving that to you.
answered Apr 1 '15 at 0:59
Daniel
5,64521639
add a comment |
up vote
0
down vote
If you define a right angle as the bisector of a straight angle - analogous to the idea of folding over a straight edge to get a fold perpendicular to that fold, with the same angle either side of the fold line to the straight line - it is clear that since straight lines are taken as similar, and you can create a straight angle by placing a point on a straight line, all bisectors of straight angles - all right angles - are also congruent.
answered Feb 1 '17 at 9:28
Joffan
32k43169
add a comment |
up vote
0
down vote
A straight angle has two right angles. If two angles are such that a supplement of the one equals itself then each must be a right angle. Since only a single parameter is involved congruence is established.
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
add a comment |
up vote
0
down vote
By supplements do you mean they sum to 180 degrees or would form a line if they were adjacent? Have you considered a proof by contradiction? I love those! Then you could assume you have two right angles which are not congruent. Going that route we are given angle A is a right angle, angle 1 is a right angle, and angle A is not congruent to angle 1. Then there exists angle B which is a congruent supplement and linear pair to angle A and angle 2 which is a congruent supplement and linear pair to angle 1. Assuming that all lines are the same degrees (180 or whatever), angle B and angle 2 are both half lines (90 degrees or whatever). So angle B and angle 2 have the same measure and are congruent, which should bring about our contradiction. Angle A is congruent to angle B, angle B is congruent to angle 2, angle 2 is congruent to angle 1, so angle A is congruent to angle 1, except that it isn't by definition. Might have to do a little cleaning up in the middle there if you move from congruence to numbers and back.
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
add a comment |
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
We say that the angle $measuredangle AOB$ is the supplement of the angle $measuredangle Y$ if the latter is congruent to an adjacent angle $measuredangle BOC$ to $measuredangle AOB$ such that the points $A$, $O$ and $C$ are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements (by definition), you can prove that all right angles are congruent as follows:
Let $measuredangle AOB$ be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let $measuredangle BOC$ be an adjacent supplement of $measuredangle AOB$, then $measuredangle AOB cong measuredangle BOC$ and $A$, $0$, $C$ are colineal.
Now let $Y$ be any other right angle and consider $D$ an exterior point of $measuredangle AOB$ such that $measuredangle AOD$ is a right angle congruent to $Y$. Here you have to prove that: $B$, $O$ and $D$ are colineal and once you have this prove that $measuredangle AOBcong measuredangle AOD$ (using "vertex opposites" arguments), I'm leaving that to you.
answered Apr 1 '15 at 0:59
Daniel
5,64521639
add a comment |
up vote
0
down vote
We say that the angle $measuredangle AOB$ is the supplement of the angle $measuredangle Y$ if the latter is congruent to an adjacent angle $measuredangle BOC$ to $measuredangle AOB$ such that the points $A$, $O$ and $C$ are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements (by definition), you can prove that all right angles are congruent as follows:
Let $measuredangle AOB$ be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let $measuredangle BOC$ be an adjacent supplement of $measuredangle AOB$, then $measuredangle AOB cong measuredangle BOC$ and $A$, $0$, $C$ are colineal.
Now let $Y$ be any other right angle and consider $D$ an exterior point of $measuredangle AOB$ such that $measuredangle AOD$ is a right angle congruent to $Y$. Here you have to prove that: $B$, $O$ and $D$ are colineal and once you have this prove that $measuredangle AOBcong measuredangle AOD$ (using "vertex opposites" arguments), I'm leaving that to you.
answered Apr 1 '15 at 0:59
Daniel
5,64521639
add a comment |
up vote
0
down vote
up vote
0
down vote
We say that the angle $measuredangle AOB$ is the supplement of the angle $measuredangle Y$ if the latter is congruent to an adjacent angle $measuredangle BOC$ to $measuredangle AOB$ such that the points $A$, $O$ and $C$ are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements (by definition), you can prove that all right angles are congruent as follows:
Let $measuredangle AOB$ be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let $measuredangle BOC$ be an adjacent supplement of $measuredangle AOB$, then $measuredangle AOB cong measuredangle BOC$ and $A$, $0$, $C$ are colineal.
Now let $Y$ be any other right angle and consider $D$ an exterior point of $measuredangle AOB$ such that $measuredangle AOD$ is a right angle congruent to $Y$. Here you have to prove that: $B$, $O$ and $D$ are colineal and once you have this prove that $measuredangle AOBcong measuredangle AOD$ (using "vertex opposites" arguments), I'm leaving that to you.
answered Apr 1 '15 at 0:59
Daniel
5,64521639
We say that the angle $measuredangle AOB$ is the supplement of the angle $measuredangle Y$ if the latter is congruent to an adjacent angle $measuredangle BOC$ to $measuredangle AOB$ such that the points $A$, $O$ and $C$ are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements (by definition), you can prove that all right angles are congruent as follows:
Let $measuredangle AOB$ be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let $measuredangle BOC$ be an adjacent supplement of $measuredangle AOB$, then $measuredangle AOB cong measuredangle BOC$ and $A$, $0$, $C$ are colineal.
Now let $Y$ be any other right angle and consider $D$ an exterior point of $measuredangle AOB$ such that $measuredangle AOD$ is a right angle congruent to $Y$. Here you have to prove that: $B$, $O$ and $D$ are colineal and once you have this prove that $measuredangle AOBcong measuredangle AOD$ (using "vertex opposites" arguments), I'm leaving that to you.
answered Apr 1 '15 at 0:59
Daniel
5,64521639
edited Apr 1 '15 at 2:03
answered Apr 1 '15 at 0:59
Daniel
5,64521639
answered Apr 1 '15 at 0:59
Daniel
5,64521639
answered Apr 1 '15 at 0:59
Daniel
5,64521639
5,64521639
add a comment |
add a comment |
up vote
0
down vote
If you define a right angle as the bisector of a straight angle - analogous to the idea of folding over a straight edge to get a fold perpendicular to that fold, with the same angle either side of the fold line to the straight line - it is clear that since straight lines are taken as similar, and you can create a straight angle by placing a point on a straight line, all bisectors of straight angles - all right angles - are also congruent.
answered Feb 1 '17 at 9:28
Joffan
32k43169
add a comment |
up vote
0
down vote
If you define a right angle as the bisector of a straight angle - analogous to the idea of folding over a straight edge to get a fold perpendicular to that fold, with the same angle either side of the fold line to the straight line - it is clear that since straight lines are taken as similar, and you can create a straight angle by placing a point on a straight line, all bisectors of straight angles - all right angles - are also congruent.
answered Feb 1 '17 at 9:28
Joffan
32k43169
add a comment |
up vote
0
down vote
up vote
0
down vote
If you define a right angle as the bisector of a straight angle - analogous to the idea of folding over a straight edge to get a fold perpendicular to that fold, with the same angle either side of the fold line to the straight line - it is clear that since straight lines are taken as similar, and you can create a straight angle by placing a point on a straight line, all bisectors of straight angles - all right angles - are also congruent.
answered Feb 1 '17 at 9:28
Joffan
32k43169
If you define a right angle as the bisector of a straight angle - analogous to the idea of folding over a straight edge to get a fold perpendicular to that fold, with the same angle either side of the fold line to the straight line - it is clear that since straight lines are taken as similar, and you can create a straight angle by placing a point on a straight line, all bisectors of straight angles - all right angles - are also congruent.
answered Feb 1 '17 at 9:28
Joffan
32k43169
answered Feb 1 '17 at 9:28
Joffan
32k43169
answered Feb 1 '17 at 9:28
Joffan
32k43169
answered Feb 1 '17 at 9:28
Joffan
32k43169
32k43169
add a comment |
add a comment |
up vote
0
down vote
A straight angle has two right angles. If two angles are such that a supplement of the one equals itself then each must be a right angle. Since only a single parameter is involved congruence is established.
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
add a comment |
up vote
0
down vote
A straight angle has two right angles. If two angles are such that a supplement of the one equals itself then each must be a right angle. Since only a single parameter is involved congruence is established.
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
add a comment |
up vote
0
down vote
up vote
0
down vote
A straight angle has two right angles. If two angles are such that a supplement of the one equals itself then each must be a right angle. Since only a single parameter is involved congruence is established.
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
A straight angle has two right angles. If two angles are such that a supplement of the one equals itself then each must be a right angle. Since only a single parameter is involved congruence is established.
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
answered Jul 20 '17 at 15:08
Narasimham
20.4k52158
20.4k52158
add a comment |
add a comment |
up vote
0
down vote
By supplements do you mean they sum to 180 degrees or would form a line if they were adjacent? Have you considered a proof by contradiction? I love those! Then you could assume you have two right angles which are not congruent. Going that route we are given angle A is a right angle, angle 1 is a right angle, and angle A is not congruent to angle 1. Then there exists angle B which is a congruent supplement and linear pair to angle A and angle 2 which is a congruent supplement and linear pair to angle 1. Assuming that all lines are the same degrees (180 or whatever), angle B and angle 2 are both half lines (90 degrees or whatever). So angle B and angle 2 have the same measure and are congruent, which should bring about our contradiction. Angle A is congruent to angle B, angle B is congruent to angle 2, angle 2 is congruent to angle 1, so angle A is congruent to angle 1, except that it isn't by definition. Might have to do a little cleaning up in the middle there if you move from congruence to numbers and back.
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
add a comment |
up vote
0
down vote
By supplements do you mean they sum to 180 degrees or would form a line if they were adjacent? Have you considered a proof by contradiction? I love those! Then you could assume you have two right angles which are not congruent. Going that route we are given angle A is a right angle, angle 1 is a right angle, and angle A is not congruent to angle 1. Then there exists angle B which is a congruent supplement and linear pair to angle A and angle 2 which is a congruent supplement and linear pair to angle 1. Assuming that all lines are the same degrees (180 or whatever), angle B and angle 2 are both half lines (90 degrees or whatever). So angle B and angle 2 have the same measure and are congruent, which should bring about our contradiction. Angle A is congruent to angle B, angle B is congruent to angle 2, angle 2 is congruent to angle 1, so angle A is congruent to angle 1, except that it isn't by definition. Might have to do a little cleaning up in the middle there if you move from congruence to numbers and back.
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
add a comment |
up vote
0
down vote
up vote
0
down vote
By supplements do you mean they sum to 180 degrees or would form a line if they were adjacent? Have you considered a proof by contradiction? I love those! Then you could assume you have two right angles which are not congruent. Going that route we are given angle A is a right angle, angle 1 is a right angle, and angle A is not congruent to angle 1. Then there exists angle B which is a congruent supplement and linear pair to angle A and angle 2 which is a congruent supplement and linear pair to angle 1. Assuming that all lines are the same degrees (180 or whatever), angle B and angle 2 are both half lines (90 degrees or whatever). So angle B and angle 2 have the same measure and are congruent, which should bring about our contradiction. Angle A is congruent to angle B, angle B is congruent to angle 2, angle 2 is congruent to angle 1, so angle A is congruent to angle 1, except that it isn't by definition. Might have to do a little cleaning up in the middle there if you move from congruence to numbers and back.
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
By supplements do you mean they sum to 180 degrees or would form a line if they were adjacent? Have you considered a proof by contradiction? I love those! Then you could assume you have two right angles which are not congruent. Going that route we are given angle A is a right angle, angle 1 is a right angle, and angle A is not congruent to angle 1. Then there exists angle B which is a congruent supplement and linear pair to angle A and angle 2 which is a congruent supplement and linear pair to angle 1. Assuming that all lines are the same degrees (180 or whatever), angle B and angle 2 are both half lines (90 degrees or whatever). So angle B and angle 2 have the same measure and are congruent, which should bring about our contradiction. Angle A is congruent to angle B, angle B is congruent to angle 2, angle 2 is congruent to angle 1, so angle A is congruent to angle 1, except that it isn't by definition. Might have to do a little cleaning up in the middle there if you move from congruence to numbers and back.
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
answered Oct 19 at 16:33
Jason Makepeace Rancho HS
1
1
add a comment |
add a comment |
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1
What is your definition of Right Angle?
– Daniel
Apr 1 '15 at 0:00
1
an angle that is congruent to one of its supplements
– user217443
Apr 1 '15 at 0:07
if it helps, I have already proven that an angle congruent to a right angle, is also a right angle.
– user217443
Apr 1 '15 at 0:07
Don't have that yet
– user217443
Apr 1 '15 at 0:26
10
In the context of Eulid's Elements, this is a Postulate.
– André Nicolas
Apr 1 '15 at 1:26