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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: astone788 on November 01, 2012, 09:53:56 pm

Title: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 09:53:56 pm: Need help with this question: VCAA further 1 2011
To makes things clear I have oriented the triangles so that they align. By doing this we can see that the corresponding sides do not match up. So how on Earth are these two triangles similar?
(http://s15.postimage.org/cxf8mspkr/similar.png)
Title: Re: SIMILAR TRIANGLES!!!
Post by: StumbleBum on November 01, 2012, 09:59:39 pm: No, you aligned the triangles wrong. You must flip it so the angle is in the same position and so that it remains connected to the point A in the same way that the bigger triangle is, if that makes sense?

So in turn the side 24, would actually be on the bottom. Then using the scale factor you will get $\frac{40}{24} = \frac{5}{3}$ which you then need to square as we are working with area, so $(\frac{5}{3})^2 \approx 2.78$ then you times this by the original 100cm^2 and you get 278cm^2, the answer.
Title: Re: SIMILAR TRIANGLES!!!
Post by: Daenerys Targaryen on November 01, 2012, 10:00:09 pm: the smaller triangle make the A at the top and D at the left bottom and B leave it
Title: Re: SIMILAR TRIANGLES!!!
Post by: TheRajinator on November 01, 2012, 10:01:40 pm: They do match just check where the hypotenous is. the orientation of your triangle is incorrect. The AB side should be on the top.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:03:12 pm: really hard to flip the triangles by imigination. Can we bring in scissors and paper to cut out triangles, to remove the guess work. Especially when your in a hurry, theres bound to be human error. Cutting out triangles would remove human error. Can't beleive no one has brang this up.

EDIT: I tried rotating it, but I still cant seem to orient it properly. The only way to do it properly is to flip the triangle like a pancake. But in my experience, whenever I do this, it doesn't work out. wtf?
(http://s12.postimage.org/amgjdg74d/similar.png)
Title: Re: SIMILAR TRIANGLES!!!
Post by: StumbleBum on November 01, 2012, 10:05:18 pm: Quote from: astone788 on November 01, 2012, 10:03:12 pm
really hard to flip the triangles by imigination. Can we bring in scissors and paper to cut out triangles, to remove the guess work. Especially when your in a hurry, theres bound to be human error. Cutting out triangles would remove human error. Can't beleive no one has brang this up.
You could remove the human error by realising that the only two common points (A and B) must be in the same position (along with the angle) for them to be similar. Drawing out the altered triangle was a good idea, you just dint pick up on your mistake of putting A on the bottom.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:10:22 pm: Quote from: StumbleBum on November 01, 2012, 10:05:18 pm
the only two common points (A and B) must be in the same position (along with the angle) for them to be similar.
??? can you illustrate this plz.
Title: Re: SIMILAR TRIANGLES!!!
Post by: StumbleBum on November 01, 2012, 10:14:50 pm: Quote from: astone788 on November 01, 2012, 10:10:22 pm
Quote from: StumbleBum on November 01, 2012, 10:05:18 pm
the only two common points (A and B) must be in the same position (along with the angle) for them to be similar.
??? can you illustrate this plz.

Sorry i men't that the only common point is A and the angle, therefore they must both be in the same position on each triangle for them to be similar. That should make more sense?
Title: Re: SIMILAR TRIANGLES!!!
Post by: Conic on November 01, 2012, 10:15:25 pm: Here's my working:
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:24:28 pm: still dont see how these triangles are similar. I rotate and orient the triangles, however the sides and angles do not correspond.
(http://s10.postimage.org/dmonlo2ix/similar.png)
Title: Re: SIMILAR TRIANGLES!!!
Post by: Conic on November 01, 2012, 10:27:37 pm: VCAAs diagrams are not necessarily scaled accurately. Check my working.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:33:28 pm: I dont know man. Harderest question I've ever seen in my life.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:39:09 pm: Quote from: Ochlocracy on November 01, 2012, 10:27:37 pm
VCAAs diagrams are not necessarily scaled accurately.
Looking at my textbook I've never seen a question like this. I guess it's best not to think too much and go with the flow regardless that it doesnt hold true to the law of similar triangles.
Title: Re: SIMILAR TRIANGLES!!!
Post by: Conic on November 01, 2012, 10:42:14 pm: But they are similar? It does hold up.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 10:44:39 pm: How?? When you orient the figures together, there are no two corresponding sides e.g.
(http://s16.postimage.org/6vjyrubed/similar.png)
we need two corresponding lengths to establish the scale factor between two similar triangles.
Title: Re: SIMILAR TRIANGLES!!!
Post by: Felicity Wishes on November 01, 2012, 10:54:34 pm: You only have like 3 values so what the triangle looks like its not that important. You have a big value (40) and a little one (24) so you go 40/24 and find the scale factor, square it and times it by 100 to find the area of bigger triangle. See how with this solution you didn't really need to move around the triangle.
Title: Re: SIMILAR TRIANGLES!!!
Post by: Conic on November 01, 2012, 10:59:32 pm: BAD is similar to CAB, not DAB and DBC.
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 11:00:46 pm: Damn. This stuff is more confusing then women. Maybe I'm analysing this too much. This is what happens when you stay in your room studying all day long :-\
Title: Re: SIMILAR TRIANGLES!!!
Post by: astone788 on November 01, 2012, 11:02:00 pm: Appreciate your help ocholocracy. Hope you do good tommorow my dude. Now get some sleep. I better not keep u up all night ;)
Title: Re: SIMILAR TRIANGLES!!!
Post by: Conic on November 01, 2012, 11:06:43 pm: Lol, I don't do further. Thanks though :)