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Sedbober [7]
3 years ago
10

In the beginning steps of constructing a perpendicular bisector of CD, the compass should be stretched out

Mathematics
1 answer:
cupoosta [38]3 years ago
8 0

Given:

Line segment is CD.

To find:

The beginning steps of constructing a perpendicular bisector of CD.

Solution:

To draw a perpendicular bisector of a line segment, first we need to open the compass more than half of the distance between the end points of the segment.

End points of the segment CD are C and D.

So, to draw a perpendicular bisector of CD, the compass should be stretched out  more than halfway from point C to the other endpoint D.

Therefore, the correct option is C.

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Rather than trying to guess and check, we can actually construct a counterexample to the statement.

So, what is an irrational number? The prefix "ir" means not, so we can say that an irrational number is something that's not a rational number, right? Since we know a rational number is a ratio between two integers, we can conclude an irrational number is a number that's not a ratio of two integers. So, an easy way to show that not all square roots are irrational would be to square a rational number then take the square root of it. Let's use three halves for our example:

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So clearly 9/4 is a counterexample to the statement. We can also say something stronger: All squared rational numbers are not irrational number when rooted. How would we prove this? Well, let \frac{a}{b} be a rational number. That would mean, \frac{a^2}{b^2}, would be a/b squared. Taking the square root of it yields:

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