congruent triangles

[Steven G]

I have to give the obvious.
The opposite angles are congruent, please look at W

 

[rachelmaddie]

I have to give the obvious.
The opposite angles are congruent, please look at W

I have to give the obvious.
The opposite angles are congruent, please look at W

angle U= angle Y
angle UWV= angle YWX
UW=VW
By AAS or ASA, two triangles are congruent.

 

[lev888]

angle U= angle Y
angle UWV= angle YWX
UW=VW
By AAS or ASA, two triangles are congruent.

Please double check #3 and provide the reason for each statement.

 

[rachelmaddie]

Please double check #3 and provide the reason for each statement.

Specifically, how do I provide reasoning?

 

[Deleted member 4993]

Specifically, how do I provide reasoning?

Have you taken a formal course in geometry?

There you would have learned about two-column proof.

 

[lev888]

Specifically, how do I provide reasoning?

You listed the 3 statements in the last post either as a random guess (I doubt it) or there were specific reasons for each one. So, assuming you didn't just guess, please post those reasons.

 

[rachelmaddie]

You listed the 3 statements in the last post either as a random guess (I doubt it) or there were specific reasons for each one. So, assuming you didn't just guess, please post those reasons.

Yes, the triangles in the figure are congruent.
angle U= angle Y
angle UWV= angle YWX
UW=VW
By AAS or ASA, two triangles are congruent.

What am I missing?

 

[lev888]

angle U= angle Y -- yes
angle UWV= angle YWX -- yes, why?
UW=VW -- why???? I asked to double check this statement. Did you?

 

[rachelmaddie]

angle U= angle Y -- yes
angle UWV= angle YWX -- yes, why?
UW=VW -- why???? I asked to double check this statement. Did you?

Double checking it would the third statement be UW = WY and isn’t the asa theorem the reasoning?

 

[lev888]

Double checking it would the third statement be UW = WY and isn’t the asa theorem the reasoning?

ASA theorem needs equal angle, side, angle. You need to prove that they are equal - that's the 3 statements with reasons. Then you can use the theorem to prove that the triangles are congruent.

 

[hoosie]

 

[rachelmaddie]

View attachment 15305

What does d(UW = d(WY) mean?

 

[hoosie]

What does d(UW = d(WY) mean?

d(UW) = UW = length of line segment UW

 

[rachelmaddie]

d(UW) = UW = length of line segment UW

Does this work?

angle U= angle Y
angle UWV= angle YWX
<UWV is vertically opposite <XWY
Also <VUW = <XYW
UW=VW
This gives two angles and a side which are the same for each triangle. Therefore we can say that two angles and the side in between of <VUW are congruent to the corresponding two angles and the side in between <YWX.
By ASA(angle side angle), the two triangles are congruent

 

[hoosie]

Should read:

angle VUW = angle XYW (angle VUW = angle U, angle XYW = angle Y)
angle UWV= angle YWX as they are vertically opposite angles.
UW=WY (UW = VW if triangle VUW is isosceles but this is not the case)
This gives two angles and a side which are the same for each triangle. Therefore we can say that two angles and the side in between of triangle VUW are congruent to the corresponding two angles and the side in between of triangle YWX.
By ASA(angle side angle), the two triangles are congruent.