# Enter the proportional segment lengths into the boxes to verify that ¯¯¯QS¯∥MN¯ . ___ /1.5= ___ / ___?

Two triangles RMN & RQS are similar.

Therefore, QS // MN.

To prove QS is parallel to MN.

That means both the triangles RMN & RQS are similar and hence MN // QS.

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To verify that ( \overline{QS} ) is parallel to ( \overline{MN} ), we need to compare the proportional segment lengths of corresponding segments.

Let's denote the lengths as follows:

Length of ( \overline{QS} ) = ( x )

Length of ( \overline{MN} ) = ( 1.5 )

Given that the segments are parallel, the proportional segment lengths must be equal.

So, we set up the proportion:

[
\frac{x}{1.5} = \frac{* }{*}
]

To solve for the missing lengths, we'll simply multiply both sides by ( 1.5 ):

[
x = 1.5 \times \frac{* }{*}
]

Once you provide the missing lengths, we can solve for ( x ) and determine if the segments are indeed parallel.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners at points A, B, and C. Side AB has a length of #27 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #18 #, what is the length of side BC?
- Triangle A has an area of #9 # and two sides of lengths #6 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has sides of lengths #18 ,3 3 #, and #21 #. Triangle B is similar to triangle A and has a side of length #14 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #16 #. If side AC has a length of #32 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #6 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #9 #, what is the length of side BC?

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