Question

Which statements must be true?

Select each correct answer.

Responses

ST=2ON
s t is equal to 2 o n

ON=12SU
o n is equal to one half s u

NO=NM
n o is equal to n m

OM¯¯¯¯¯¯∥TU¯¯¯¯¯
segment o m is parallel to segment t u

MN¯¯¯¯¯¯¯∥SU¯¯¯¯¯
segment m n is parallel to segment s u
The figure shows what appears to be acute triangle S T U. Point M is on side S T. Single tick marks pass through segments S M and M T. Point N is on side T U. Double tick marks pass through segments T N and N U. Point O is on side U S. Triple tick marks pass through segments U O and O S. Segments M N, N O, and O M are drawn.

Answer 1

Correct answers: ST = 2 ON; OM ∥ TU; MN ∥ SU.

Reason: The tick marks show M, N, O are midpoints of ST, TU, and US. By the Midpoint (midsegment) Theorem, a segment joining midpoints of two sides of a triangle is parallel to the third side and half its length. Thus
- NO = 1/2 ST, so ST = 2·ON (true).
- OM connects midpoints of US and ST, so OM ∥ TU (true).
- MN connects midpoints of ST and TU, so MN ∥ SU (true).

The others are not necessarily true: ON = 1/2 SU would require ST = SU, and NO = NM would require ST = SU, which need not hold in a general triangle.