Enter the proportional segment lengths into the boxes to verify that ¯¯¯QS¯∥MN¯ .

___ /1.5= ___ / ___?

Question

James Atkins · Accepted Answer

Two triangles RMN & RQS are similar.
Therefore, QS // MN.

To prove QS is parallel to MN. #9/1.5 = 12/2 = 6/1# #:. (RM) / (MQ) = (RN) / (NS) color (white)(aaa) Eqn (1)# Add 1 to both sides, #( (RM) + (MQ) ) / ( MQ) = ((RN) + (NS))/ (NS)# #(RQ) / (MQ) = (RS) / ( NS) color (white)(aaa) Eqn (2)# Dividing Eqn (1) by (2), #(RM) / ( RQ) = (RN) / ( RS)# Two sides of triangles RMN & RQS are in the same proportion. Therefore third sides are also in the same proportion. #:. (MN) / ( QS) = (RM) / ( RQ) = (RN) / ( RS)# That means both the triangles RMN & RQS are similar and hence MN // QS.

Autumn Armstrong · Answer

undefined 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.

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

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