Answer:
The correct option is 1.
Step-by-step explanation:
It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.
It triangle RST and SUT,
[tex]\angle RST=\angle SUT=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle STR=\angle UTS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle SUT[/tex] .... (1)
It triangle RST and RUS,
[tex]\angle RST=\angle SUR=90^{\circ}[/tex] (Definition of altitude)
[tex]\angle SRT=\angle URS[/tex] (Common angle)
Two corresponding angles are equal. So by AA property of similarity,
[tex]\triangle RST\sim \triangle RUS[/tex] .... (2)
According to transitive property of equality,
if a=b and b=c, then a=c.
From (1) and (2), we get
[tex]\triangle RUS\sim \triangle SUT[/tex] ( Transitive property of equality)
Therefore the correct option is 1.
