Number of drawable triangles

[Jupiter]

How many triangles can be drawn in the following situations:

1)Two angles of a triangle are 60 and 70 and one of the sides is 5 cm.

2)Triangle MNP: N= 27.5 (degree) P=1.5 (degree) MN=30 cm

3)Triangle ABC: C = 29 (degrees) AC=10 cm AB=7 cm

4)Triangle ABC: A = 5 (degree B = 20 degree BC = 4 cm

5)Triangle ABC: A= 40 (degree BC = 3 cm AB=2.5 cm

6)Triangle ABC: A= 40 (degree BC = 3 cm AB=5 cm

7)Triangle ABC: B= 130 degree BC = 8 cm C = 30 degree

 

[Dr.Peterson]

How many triangles can be drawn in the following situations:

1)Two angles of a triangle are 60 and 70 and one of the sides is 5 cm.

2)Triangle MNP: N= 27.5 (degree) P=1.5 (degree) MN=30 cm

3)Triangle ABC: C = 29 (degrees) AC=10 cm AB=7 cm

4)Triangle ABC: A = 5 (degree B = 20 degree BC = 4 cm

5)Triangle ABC: A= 40 (degree BC = 3 cm AB=2.5 cm

6)Triangle ABC: A= 40 (degree BC = 3 cm AB=5 cm

7)Triangle ABC: B= 130 degree BC = 8 cm C = 30 degree

Have you tried?

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For example, on (1), if the given angles are at A and B, you might try making AB, BC, or AC equal to 5 cm. Do they all work?

Please show us what you've done and where you need help.

 

[The Highlander]

How many triangles can be drawn in the following situations:

1)Two angles of a triangle are 60 and 70 and one of the sides is 5 cm.

2)Triangle MNP: N= 27.5 (degree) P=1.5 (degree) MN=30 cm

3)Triangle ABC: C = 29 (degrees) AC=10 cm AB=7 cm

4)Triangle ABC: A = 5 (degree B = 20 degree BC = 4 cm

5)Triangle ABC: A= 40 (degree BC = 3 cm AB=2.5 cm

6)Triangle ABC: A= 40 (degree BC = 3 cm AB=5 cm

7)Triangle ABC: B= 130 degree BC = 8 cm C = 30 degree

Hi @Jupiter,

You have posted what looks like a Maths question that might be given to a pupil aged 11 to 13 years. Is that correct?

However, you do not tell us why you have posted this question!

Were you just hoping that someone in the forum would do it for you? I am afraid that is unlikely as the forum ‘rules’ forbid members from simply posting the answers to questions submitted; we are limited to offering help or advice only, not answers.

Since you do not tell us why you have posted this question, ie: why you cannot do it yourself, then we can only guess what your problem is and, therefore, how best to help or advise you.

I would, therefore, assume that you are in the age bracket I mentioned above and that the best way to help you is to go over some basic points about how we deal with triangles in Maths and give you an example of how to tackle this question.

Unfortunately, the question is very poorly written!

Whereas it says: “How many triangles can be drawn in the following situations:”, I think it ought to say: “How many different triangles can be drawn in the following situations:”!

You could, in practice, draw as many triangles as you liked in any of the “situations” provided but many of them would just be the same triangle drawn in a slightly different orientation, eg: if you a draw a triangle then draw the same triangle but turn it through 90° then it is not a different triangle (even though it might look different).

So let us, first of all, assume that the question writer actually meant to ask: “How many different triangles can be drawn in the following situations:”.

Secondly, the question, as written, only requires you to provide a number (eg: 1, 2, 3, etc.) as the answer to each part but I suspect that the intention is to get you to actually construct (draw) the different ‘possible’ triangles for each situation given. It may also be that you are expected to do this accurately using a ruler & protractor but, if that is not a requirement (your teacher would probably tell you whether or not it is) then you would likely only need to draw (rough) sketches with ‘approximate’ angles and lengths.

In my opinion, therefore, you do need to at least sketch the different triangles that are possible in each situation listed and then give that number of sketches (or drawings) as the final answer to each part. In maths we talk about a ‘sketch’ as being a drawing that is not an accurate drawing but does use good approximations to the actual dimensions (lengths & angles) specified; sketches are (usually) also much smaller than an accurate drawing would be.

So, where to begin?

Firstly, it is important to follow certain conventions (rules) that we use in Maths when constructing drawings or sketches of figures like triangles; here is a summary:-

​

Now that you know how to label a triangle correctly, let us consider an example of the type listed in the question.

If I add a new part (Part 8), I would attempt it as follows:-

​

You cannot move around or rotate the lower one so that fits exactly over the upper one so they are different triangles but if you were to flip it up it would fit exactly over it. That is because they both meet the same conditions that were given to produce them and so are said to be congruent.

So the answer to (my ‘new’) part 8) is: 2 but that answer needs to be accompanied by the sketches of those two triangles.

Another way to get the ‘second’ triangle is to “swap around” the points B & C on your 6 cm line:

​

So, what you need to do is investigate all the possibilities for different but congruent triangles (ie they all meet the given conditions) in each situation listed to come up with the answers for each part.

I hope that helps. ?

 

[Dr.Peterson]

Whereas it says: “How many triangles can be drawn in the following situations:”, I think it ought to say: “How many different triangles can be drawn in the following situations:”!

So, what you need to do is investigate all the possibilities for different but congruent triangles (ie they all meet the given conditions) in each situation listed to come up with the answers for each part.

My guess is different; I imagine the problem as being given either in geometry or trigonometry in connection with theorems like SAS and SSA, and that the intent is to count the number of different (in the sense of non-congruent) triangles that satisfy the conditions. It may be helpful to sketch them, but may not be necessary.

But we don't know yet.

@Jupiter: please, in addition to showing whatever work you have tried (which I hope would give us a sense of the intent and level of the problem) tell us explicitly what you are currently studying, and perhaps how old you are, so we will be able to address any help we give to the appropriate context.

 

[Dr.Peterson]

How many triangles can be drawn in the following situations:

1)Two angles of a triangle are 60 and 70 and one of the sides is 5 cm.

2)Triangle MNP: N= 27.5 (degree) P=1.5 (degree) MN=30 cm

3)Triangle ABC: C = 29 (degrees) AC=10 cm AB=7 cm

4)Triangle ABC: A = 5 (degree B = 20 degree BC = 4 cm

5)Triangle ABC: A= 40 (degree BC = 3 cm AB=2.5 cm

6)Triangle ABC: A= 40 (degree BC = 3 cm AB=5 cm

7)Triangle ABC: B= 130 degree BC = 8 cm C = 30 degree

Since you haven't yet responded to our requests for more information, I want to be more direct.

Are you studying geometry, or trigonometry?

Have you learned about the SAS, ASA, AAS, SSS, and SSA cases?

Have you tried either drawing the triangles, or using trig to solve the triangles, or applying the theorems you have been given? I want to know what you have learned so I can help you do that, and not something else that would not be suitable for you.

In particular, several of these triangles are the SSA case, in which there could be either 0, 1, or 2 different (non-congruent) triangles that satisfy the conditions. What have you learned about that?