Problem W, Part (i)
The order of the letters is very important when it comes to figuring out similarity statements. This is because the angles must match up. Recall that similar triangles have corresponding angles that are congruent.
The diagram shows that
A = 60 and E = 60
Since A is listed first in ABC, this means E must be listed first in the answer.
Then we'll have D listed next because B = 55 and D = 55 are congruent angles.
The last remaining letter is C. Therefore, the correct sequence is EDC
Answer: EDC
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Problem W, Part (ii)
Like with the previous part, the order is important. Not only to help match up corresponding angles, but also to pair up the corresponding sides as well.
- AB = 12 mentions the first two letters of ABC
- ED = 16 mentions the first two letters of EDC
both of those mention the first two letters of their triangle name.
This then leads to AB/ED being one ratio we can form.
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AC = 10 mentions the first and last letters of ABC
EC = x mentions the first and last letters of EDC. Note that EC is the same as CE.
So we can form AC/EC as another ratio. The key here is that this ratio is equal to the other ratio AB/ED we formed earlier (or else the triangles wouldn't be similar)
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The takeaway from those last two sections is that we can form this proportion
AB/ED = AC/EC
Apply substitution and solve for x
AB/ED = AC/EC
12/16 = 10/x
12x = 16*10 ... cross multiplication
12x = 160
x = 160/12
x = 40/3
x = 13.333 approximately
Answer in fraction form = 40/3
Answer in decimal form = 13.333
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Problem W, Part (iii)
This part isn't too lengthy compared to part (ii). All we simply do here is divide any side of triangle EDC by its corresponding side of triangle ABC.
The easiest in my opinion is to pick on sides that are already mentioned in the diagram, so we could say:
scale factor = ED/AB = 16/12 = 4/3 = 1.33 which is approximate.
The scale factor indicates that triangle EDC has its side lengths roughly 1.33 times larger compared to the corresponding side lengths of triangle ABC.
Any time the scale factor is larger than 1, it means the image is going to be larger compared to its preimage. If the scale factor was between 0 and 1, excluding both endpoints, then the image would be smaller than its preimage.
Answer in fraction form = 4/3
Answer in decimal form = 1.33
