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We disagree with John's statement.
With reference to the diagram in draft 2, from the above we can see that :
AB=A'B'
AC=A'C'
∠ABC=∠A'B'C'
However，
BC≠B'C'
∠ACB≠∠A'B'C'
∴，we can see that the 2 triangles cannot be congruent as the ∠ABC is not the same.Thus， John is wrong

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We don't agree with George's statement.
With reference to the diagram in draft 1, from the above graph we can see that the 2 triangles ， ABC and A'B'C' are bothe similar in the angles （60º），thus ，having the same shape.
∠ABC=∠A'B'C'
∠BAC=∠B'A'C'
∠ACB=∠A'C'B
Thus，this 2 triangles are in the same shape.However，for them to be congruent，both would need to have the same size.
BC≠B'C'
Above shows that ∠ABC is bigger than ∠ABC.
∴，George's statement is incorrect thus we don't agree with it.

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https://docs.google.com/document/d/1RxAoElx24MGnyuTxfFn4mlZHl0zUkhmubdCYg5JG77E/edit?usp=sharing

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Final Copy

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Isaac Kok & Paul Mathias Lim

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Diagram 2

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Diagram 1

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The explanation for both questions are very clear and easy for me understand about why u chose that particular answer. However it could be improved more by adding more diagrams as im sure it would be much easier for everyone especially for those who don’t understand to understand it -Jia Chen

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Good explaination for both points. #opinion you could add some diagrams for the 2nd part to make it clearer. -

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a)No, I disagree with George. As when triangles are congruent, the corresponding sides are equal. Since two equilateral triangles can have sides of different lengths that are corresponding to each other. Hence, not all equilateral triangles will be congruent to each other.

b)No, I disagree with John. If two pairs of angles of two triangles are equal in measurement the third angle will also be the same due to total sum of angle in each triangle is the same. As the triangles have same measurement of angles already, when two pair of corresponding sides are equal in length, the third pair of sides will also be same so that it will be congruent. However as John only state that the pairs of lines are corresponding it may not be in the same length so the two triangles may be similar. Therefore the two triangles may are not congruent.

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No, I disagree with John. If two pairs of angles of two triangles are equal in measurement the third angle will also be the same due to total sum of angle in each triangle is the same. As the triangles have same measurement of angles already, when two pair of corresponding sides are equal in length, the third pair of sides will also be same so that it will be congruent. However as John only state that the pairs of lines are corresponding it may not be in the same length so the two triangles may be similar. Therefore the two triangles may are not congruent.

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Overall, quite clearly explained
#opinion the explanation for George was well written and easy to understand since there was diagrams to refer to. however, #ineedtounderstand the explanation for John better, u could add simple diagrams for examples
-isaac kok

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https://docs.google.com/document/d/1b6dWdZgCxdpSlQlMPkH48qqhZauYPHsQBknaRUhZehk/edit?usp=sharing

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I disagree with George's statement when he said that all equilateral triangles are congruent to each other.All equilateral triangles have 3 60 degrees.However,equilateral triangles might not mean that they have the same side even if they have the same angles.Same angles but different lengths are not considered to be congruent but only similar.

We also disagree with John's statement.Although 2 triangles have two similar sides and one same non-included angle,does not mean that they are congruent to one another.As shown in the new drawing of the two triangles below,we can clearly see that both of the triangles have two similar sides and one similar non-included angle,they are still different as one of the last side of both triangles may be different and the two included angles can be different as well.

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https://docs.google.com/document/d/1_XlIC_gn2lwU1X7kh7xvtLuSpph_LJVM7ILEKd3sWs4/edit?usp=sharing

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This explanation was done nicely. I liked that you included several diagrams to prove your point. However, my suggestion would be to organise the triangles such that they are lined up and improve on the paragraph format by making it more neat.

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I disagree with John's statement.
From the figure below you can see that 2 pairs of corresponding sides and a pair if non-included angles will not give you the same triangle.
The known non-included angle will be the total of the 2 left angles in the triangle. The interior angles Have a wide range of possibilities since the 3rd line can be as long or as short as necessary. wide range of possibility
The figure below illustrates 1 such case:

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I do not agree with George's statement.
Although all equilateral triangles may all share the same angles but their lengths might differ greatly. The equilateral triangle can only go so far to be similar to each other unless all their lengths are equal to each other.

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Final copy

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I think you can explain more on why George's statement is incorrect as I feel like the answer is not fully elaborated. Yes, equilateral triangles are similar and not congruent, however, you can further explain on why they are not congruent rather than jumping into the conclusion of saying that you disagree with George's statement.
-Alexis :))

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In my #opinion , the diagrams are neat and clearly drawn by using different letters and keys. I could understand what you’re trying to say as the explanations are well elaborated. ~Jinyi

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ISABEL,TELL SHENPAI SHE OWES ME TWO CHICKEN PIES

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i ship you guys ( ͡° ͜ʖ ͡°)

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ANNABELLE AND jun cheng,hmm,more like
ANNABELLE X JUN CHENG

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#GoodJob  The explanation is clear and the accompanying diagrams are nicely drawn.
#Opinion I feel that the second questions could be further explained

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for john's statement,i agree with john as since the two pairs of corresponding sides and the pair of corresponding non included angles are equal.with reference to the diagram,it can be seen that they will result in two congruent triangles since the included angle at the top will result in the bottom angles being equal to each other,this means that angle xyz = angle x'y'z',angle yzx = angle y'z'x',angle zxy = angle z'x'y'.the two pairs of corresponding sides will result in the length of the base being the same for both triangles,this will mean that xy =x'y',yz =y'z',zx=z'x',since the two criteria for congruency has been satisfied with all the corresponding sides and angles being the same,i agree with john's statement

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a)I do not agree with George's  statement but agree with John's statement.

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a)I do not agree with George's  statement but agree with John's statement.

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b)For George's statement, he is incorrect as in the diagram drawn, both triangles are equilateral but have different lengths on each of their sides. Meaning that AB=BC=CA and DE=EF=FD but an y of the given sides of one triangle does not have an equal length with that of any side of the other triangle. This means that they do not satisfy the criteria for congruence as congruent figures have the same shape and size but the two triangles in the diagram only have the same shape as all their interior angles are equal but they have different lengths on each side which means that they do not satisfy the criteria for congruence. Therefore I can conclude that George's statement is incorrect.  (continuation for John's statement above)

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#opinion,this has a very detailed explanation for disproving the statements but i would like a diagram so that people can understand your explanation easily

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I agree with your statement. Overall, the whole diagram is very neatly drawn and very easy to understand but, what is SSA method?
-boonling

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#opinion
i feel that the second example was well explained using the different colours and key so that people won’t be confused. Maybe the first example could also be done in the same way. i feel that there should be a clear conclusion for the second question too -dian

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For the second part of the question involving the two provided sides and a non-included angle,the non-included angle is wrong as the non-included angle is outside the triangle but the presentation is very clear and i think the explanation can be abit more thorough so a good effort overall. ~Lester

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I do not understand what is ssa even after seeing the diagram -Hui ya

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#opinion for the 2nd diagram you should put in the angles if not i could assume that all the angles are non includent angle

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The presentation of your work is very simple and easy to read, however my #opinion is that with the examples that are given, it would be less confusing if instead of ABC and A'B'C' it was written as ABC and DEF so that it doesn't look so messy. Overall very neat and well elaborated. ~Li Xuan

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Overall, I agree with you on the statement and evidence given.The diagrams were drawn clearly and I could understand the explanation.
#INeedToUnderstand the SSA method u applied. Hence, giving the definition of the SSA method would help me understand better. In all, I feel that I could understand the diagrams, but not much of the explanation.
-Kevyn

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I agree with both your statements and explaination. However, there needs to be further elaboration. For example, #Ineedtounderstand the specific definition of congruency and similarity by stating clearly which “size of the angles” and which “length of the 3 sides” are the same, in order to understand more clearly why the statement is wrong.

#opinion I think you could have made the diagrams bigger so it is easier to view. The diagrams could have been labeled so you could give specific examples to prove why the statements are incorrect.
- Jia Le

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To be frank, I really like the way this is done. It is very detailed in the explanation and allows very easy understanding. One thing i would change is that I feel that the pictures are a little bit messy although well annotated. For example I could not really see which values match the which sides properly. But other than that, it was a really well done task

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#Opinion I think that the photo example of John's is contradicting to the explanation that is give. The answer should not be forced out randomly but can be obtained from further research.
#Furtherexplanation I think that not much explanation was written, so it is not so easy for others to understand. Explanation given should be used along with easier terms.

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you can do the workings on diagrams on a clean sheet of white paper as it would be alot clearer for us to view it. #ineedtounderstand what the SSA means, how does it  lead to your conclusion of john being half correct. Diagrams for the secong statement doesnt really help prove the claim perhaps you could give another example diagram as the non-included angles in this case seems to be an included angle. First claim was done well though , just remember to write out clearly !! - shannon

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good job on the explanation or the first question ! it was well explained:) however,for the second question it was not really very clearly explained as to why John's statement is wrong. #INeedToUnderstand why the diagrams used had led to you conclude that John's statement is incorrect. Perhaps you could say that although both triangles have two pairs of corresponding sides and a pair of non-included angles are equal, it does not show that both triangles are congruent (since they are not identical) , so as to further prove your point. i feel that the "One triangle can have an acute angle and the other can have an obtuse angle as shown in the diagram below. " is not enough to prove your point.

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#great attempt You girls used the Geogebra which is good as you put what you learn into your work. I also agree with your answers, both of the boys are wrong. #clear diagrams Nice nice diagrams to let people understand. #different opinion However I agree to your explanation to a certain extent. The last line of George statement "equilateral triangles are only congruent if the side is equal." is badly phrased. If it's me I would be careful when I use the word 'only' When you say only congruent when the side is equal you are trying to say it only have one property which is as long as the sides of both figures are the same length it is congruent? That is incorrect. The angles must be the same as well. Hence I would phrase the sentence like the sides of both figures is one of the property of congruent figures. #ineedtounderstand What is the John explanation? I cannot get what the last paragraph means. I think it lacks explanation for the last question. It would be better if you can explain why it is wrong maybe by showing the opposite instead of stating facts like what the picture shows.

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I think it is better for you guys to further explain why the equilateral triangles are similar,like with more proof.
Furthermore, i think it is a lot better to compare if you guys add one more triangle in John's case in your drawing to compare that two pairs of corresponding sides and one non-included angle do not prove that it is congruent.Highlighting that one triangle in blue and orange is harder to visualise.

Jun Cheng

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#Opinion What do you mean by "same shape"? Did you mean same angle and scale factor? Also please just type your answers into padlet instead of using microsoft word.
Other than that pretty good. I like the illustrations shown. You might also want to consider elaborating on your statements more, as your answer lacks explanation.
- Teo Tze Rey

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#INeedToUnderstand why you explain why the equilateral triangles are similar instead of congruent in George’s case
#Opinion i agree that if a side of the triangle is different, the two angles at the sides may be different, therefore i agree that the two triangles may not be congruent is John’s case
i would recommend you to draw two separate triangles instead in John’s as it may be easier to visualise
#ILearned that it is possible for two equilateral triangles with corresponding lengths to not be congruent
-anabelle

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I agree with your statements, the statements are very well explained and are very easy to understand the drawings or diagrams are drawn very clearly and are easy to understand - Kimberly

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I agree with you on the statement and evidence given. The diagrams are neatly drawn out and the proof given is easy to understand. #INeedToUnderstand how you are able to figure out the fact that two of the angles and a side of the corresponding figures must be the same in order for both of the triangles to be congruent. Overall, i think that this draft was very well thought out and explained.
-Amelia

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I also disagree with the draft 2 as the question have stated that that is a pair of lines and an angle that are the same.#keepitup Overall，I do think that you did the work really neatly and the graphs are really tidy.#thingstoimprove Although the explaination is quite okay， you should elaborate more.Keep up the good work!

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I also disagree with the dr

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I agree with ur statement and explanation. It is very clear as ur use diagrams in explaining. However I think if ur can type out ur work that will be neater to read. It is a bit hard to see on paper.

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I disagree with your draft 2.
#keepitup your diagram was neat and easy to read, but there is not enough information to prove John is correct

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The diagrams are very clear and helps to furthur explain your point.
However, can you explain more on the two explanations that you gave because I am still a bit confused by what you are trying to explain.
In overall, it is a good attempt to answer the questions.
Ling Si Jia

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Although overall this is comprehensive, I feel it would be better if you provided a diagram to show what you mean

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Although overall this is comprehensive, I feel it would be better if you provided a diagram to show what you mean

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I think I would be neater if you guys typed it out and as for the diagram, you guys could use geogebra to form the diagram. I could be neater if you can put it in paragraphs

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I agree with your statement and your explanation. The diagrams are also very well-drawn. However, #INeedToUnderstand  what the SSA method is. You could have written the definition of the SSA method so that it will be easier to understand your explanation. Similarly, you could also have included definitions for some of the key terms. But other than that, it was very well-done.
-Casey Wong

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I agree with your draft 1 that George is incorrect.
#Opinion For draft 2 I think you ca state all your angles to give your reader a clearer view of what you are trying to say
Seet E-Ling

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a) We do not agree with both George and John.
b) George is incorrect as a pair of equilateral triangles might not be congruent as they might not have the same corresponding length of the sides. As seen from diagram 1, triangle ABC is not congruent to triangle A'B'C' as AB is not equal to A'B'. Only figures with corresponding lengths and angles are congruent and since the two triangles do not have corresponding lengths, they are not congruent but similar. Thus, we can conclude that not all equilateral triangles are congruent.

John is incorrect as the pair of non-included angles may be different from the third angle in each triangle. The two pairs of corresponding sides may be the same length but in different orientations. For example, in diagram 2, both triangles are isosceles triangles with two pairs of corresponding sides and a pair of non-included angles, however, the top angle of the triangle are different which makes both the triangles not congruent. Thus, if two triangles only has 2 pairs of corresponding sides and a pair of non-included angles which are equal, they might not be congruent.

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John is correct because as seen from the diagram because AB

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#ineedhelp! Can you explain more?
#picturequality need your attention.
I can see shadows on the paper.
#makeitmoreclearer
all your diagrams need to show angles though...
Thank you for noticing this pink slip.
-Zhang Hao Dong

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https://docs.google.com/document/d/1b6dWdZgCxdpSlQlMPkH48qqhZauYPHsQBknaRUhZehk/edit?usp=sharing

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https://docs.google.com/document/d/1mH2h1WmjBj76jxLEOvg6dKz3VaZiiF-9O9Nle-Z6_xI/edit?usp=sharing