Justify the last two steps of the proof.
given rs+ut and rt=us
prove: rst=uts
rs=ut given
rt=us given
st=ts
rst=

The correct answers are:

Reflexive property; 
SSS (Side-Side-Side congruence theorem).

Explanation:

ST and TS are two ways of naming a line segment.  In this case, it is the third side of the triangle.

Saying that ST=TS says that ST is equal to itself.  This is the reflexive property.  It says that any line segment is congruent to itself.

We now have three sides of one triangle congruent to three sides of another triangle.  This is the side-side-side congruence theorem, or SSS.

The correct answers are:

Reflexive property; 
SSS (Side-Side-Side congruence theorem).

Explanation:

ST and TS are two ways of naming a line segment.  In this case, it is the third side of the triangle.

Saying that ST=TS says that ST is equal to itself.  This is the reflexive property.  It says that any line segment is congruent to itself.

We now have three sides of one triangle congruent to three sides of another triangle.  This is the side-side-side congruence theorem, or SSS.

Given RS+UT and RT=US
Prove:RST=UTS
RS=UT given
RT=US given
ST=TS reflexive property (it is just like you see in a mirror)
RST=UTS (SSS)

Given RS+UT and RT=US
Prove:RST=UTS
RS=UT given
RT=US given
ST=TS reflexive property (it is just like you see in a mirror)
RST=UTS (SSS)