Which statements must be true?

select each correct answer.

mn∥su

om∥tu

on=12su

st=2on

no=nm

The correct options are  , and ST=2ON .

Explanation:

Since, In triangle STU,  M, O and N are mid points of line ST, SU and TU respectively.( given SM=MT, TN=NU and SO=OU)

By the mid point theorem which states that the line segment joining two midpoints of two sides of a triangle must be parallel to the third side of the given triangle. And, it is half of the third side.

Since MN is a line segment which is made by mid points M and N.

So, it must be parallel to the third side SU.

Therefore,

Similarly, OM is a line segment which is made after joining mid points O and M. So, it must be parallel to third side TU.

Now,ON is a line segment which is made after joining mid points O and N. So, it must be half of the third side ST.

Therefore, ON=ST/2⇒2ON=ST

Therefore, .

Note: ON=12SU (not necessary),  NO=NM(not necessary)

1. minimum

2. 6400

3. eight

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