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olga2289 [7]
3 years ago
11

Let m,n,p, and q represent nonzero positive integers. find a number in terms of m,n,p, and q that is halfway between m/n and p/q

.
Mathematics
2 answers:
alukav5142 [94]3 years ago
7 0
This is the same as averaging. You add them and divide by 2.

((m/n) + (p/q))/2 would be a number in between m/n and p/q.

Do note that n and q must be nonzero, but luckily that is a given.
bulgar [2K]3 years ago
6 0

Answer:

it is given that,m,n,p, and q represent nonzero positive integers.

A number between a and b is given by

  \frac{a+b}{2}

where, a and b are rational numbers ,having denominator ≠0.

A number between

 \frac{m}{n} \text{and} \frac{p}{q} \text{is equal to}\\\\=\frac{\frac{m}{n} + \frac{p}{q}}{2}\\\\=\frac{mq+np}{2nq}

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Question 1

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Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles <u>are similar</u>. I used the <u>SAS similarity theorem</u>.

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Question 2

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Repeat for the other triangle as well

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Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, <u>the two triangles are similar</u>.

This time we use the <u>AA Similarity theorem</u>

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Question 4

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Question 5

Any angle is equal to itself due to the <u>reflexive property</u>. So that will go for reason number 2.

Reason 3 is <u>SAS similarity</u> because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

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