Respuesta :

Answer: The correct options are  [tex]MN\parallel SU[/tex], [tex]MO\parallel TU[/tex] 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, [tex]MN\parallel SU[/tex]

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, [tex]MO\parallel TU[/tex] .

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

The true statements about the given triangle are;

MN∥SU

OM∥TU

ST=2ON

In triangle STU given, we see that;

M, O and N is the mid point of ST

O is the mid point of SU

N is the mid point of TU.

Thus;

SM = MT

TN = NU

SO = OU

Let us look at the options;

A) MN∥SU; This is true because from the midpoint theorem, we see that MN is a line segment joining the midpoints M and N of two sides of the triangle and thus it must be parallel to the third side SU.

B) OM∥TU; This is true also because from the midpoint theorem, we see that OM is a line segment joining the midpoints O and M of two sides of the triangle and thus it must be parallel to the third side TU.

C) ON = 1/2 SU; This is not true because ON is not half of SU from the diagram

D) ST = 2ON; This is true because ON is equal to MT and MT is half of ST.

E) NO = NM; This is not true because they are adjacent to each other but unequal.

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