For which segment lengths is qs¯¯¯¯¯ parallel to mn¯¯¯¯¯¯¯ ? a triangle with vertices labeled as q, r, s. side q s is base. sides r q and r s contain midpoints m and n, respectively. a line segment is drawn from m to n. select parallel or not parallel for each set of given information.

QM=2 MR=4 SN=3 NR=3) NOT Parallel

QM=2 MR=5 SN=6 NR=15) PARALLEL

QM=2 MR=8 SN=3 NR=12) PARALLEL

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[tex]For which segment lengths is qs¯¯¯¯¯ parallel to mn¯¯¯¯¯¯¯ ? a triangle with vertices labeled as q,[/tex]

Thus, (1) is non parallel set and (2) and (3) are parallel set.

Step-by-step explanation:

Consider a triangle with vertices labeled as Q, R, S. Side QS is base. Sides RQ and RS contain midpoints M and N, respectively. A line segment is drawn from M to N as shown in figure below.

For MN and QS to be parallel the ratio of line segment must be in same ratio, that is [tex]\frac{RM}{RQ}=\frac{RN}{RS}[/tex].

Check for the given options,

1) Given : QM=2, MR=4, SN=3, NR=5

Find the values in the ratio,

[tex]\frac{RM}{RQ}=\frac{RM}{RM+MQ}=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]\frac{RN}{RS}=\frac{RN}{RN+NS}=\frac{5}{8}=\frac{5}{8}[/tex]

Thus, [tex]\frac{RM}{RQ}\neq \frac{RN}{RS}[/tex]

Thus, (1) is non parallel set.

2) Given : QM=2, MR=5, SN=6, NR=15

Find the values in the ratio,

[tex]\frac{RM}{RQ}=\frac{RM}{RM+MQ}=\frac{5}{7}[/tex]

[tex]\frac{RN}{RS}=\frac{RN}{RN+NS}=\frac{15}{21}=\frac{5}{7}[/tex]

Thus, [tex]\frac{RM}{RQ}=\frac{RN}{RS}[/tex]

Thus, (2) is parallel set.

3) Given: QM=2, MR=8, SN=3, NR=12

Find the values in the ratio,

[tex]\frac{RM}{RQ}=\frac{RM}{RM+MQ}=\frac{8}{10}=\frac{4}{5}[/tex]

[tex]\frac{RN}{RS}=\frac{RN}{RN+NS}=\frac{12}{15}=\frac{4}{5}[/tex]

Thus, [tex]\frac{RM}{RQ}=\frac{RN}{RS}[/tex]

Thus, (3) is parallel set.

The given for this problem is:

QM=2, MR=4, SN=3, NR=5 QM=2, MR=5, SN=6, NR=15 QM=2, MR=8, SN=3, NR=12

So from the above question:

QM=2 MR=4 SN=3 NR=3) is not parallel

QM=2 MR=5 SN=6 NR=15) is parallel

QM=2 MR=8 SN=3 NR=12) is parallel