Determine whether each pair of triangles is similar. Justify your answer.
2 answers:
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*see attachment showing the two polygons in a grid.
Answer:
No, PQRST is not a scale copy of ABCDE because we the sides are not increased proportionally.
Step-by-step explanation:
A polygon can be said to be a scaled copy of another polygon, if the the same scale factor is used in scaling every segment of the preimage or original image to get the length of the corresponding segments of the scale copy or image. In order words, all segments must be scaled proportionally.
Polygon PQRST, which is the new image, has different scale factors used in scaling the various segments of the preimage. In simple terms, the sides of PQRST were not increased proportionally. Therefore, PQRST is not a scaled copy of ABCDE.
6. When we multiply two surdic integers, we can leave it into one big surd.
For instance, if we have:
, we can simplify it down to one uniform square root sign, 
.
So, we can say:
, which is a rational root, because the square root of 36 can be converted into an integer, namely 6 and -6.
Hence, it is a rational root.
7. The summation, on the other hand, cannot be simplified any further, so it will stay as irrational. This is because √2 is already an irrational root, and adding it onto a number that is rational will stay as irrational.
8. Once again, the summation cannot be simplified. We can only simplify by factoring like terms. Hence, this must be irrational.
9. Even if it is in fractional notation, √5 can never be a rational number because no two integers when multiplied by itself will give 5. So, even if it is written in fractional form, they cannot be rational if there is an already irrational term in it.
For instance, if we have:
So, we can say:
Hence, it is a rational root.
7. The summation, on the other hand, cannot be simplified any further, so it will stay as irrational. This is because √2 is already an irrational root, and adding it onto a number that is rational will stay as irrational.
8. Once again, the summation cannot be simplified. We can only simplify by factoring like terms. Hence, this must be irrational.
9. Even if it is in fractional notation, √5 can never be a rational number because no two integers when multiplied by itself will give 5. So, even if it is written in fractional form, they cannot be rational if there is an already irrational term in it.