# Thread: Prove ST > UV

1. ## Prove ST > UV

Given TU is congruent to US. US is congruent to SV.
Prove ST > UV.

2. Originally Posted by magentarita
Given TU is congruent to US. US is congruent to SV.
Prove ST > UV.
Are points T, U, S, and V collinear?

If so, then ST = UV.

T-----|-----U-----|-----S-----|-----V

Proof:

(1) $\displaystyle TU=US \ \ and \ \ US=SV$ GIVEN

(2) $\displaystyle TU=SV$ Transitive property of equality

(3) $\displaystyle US=US$ Reflexive property of equality

(4) $\displaystyle TU+US=SV+US$ Addition property

(5) $\displaystyle TU+US=ST \ \ and \ \ SV+US=UV$ Segment addition postulate

(6) $\displaystyle ST=UV$ Substitution (4) and (5)

Originally Posted by masters
Are points T, U, S, and V collinear?

If so, then ST = UV.

T-----|-----U-----|-----S-----|-----V

Proof:

(1) $\displaystyle TU=US \ \ and \ \ US=SV$ GIVEN

(2) $\displaystyle TU=SV$ Transitive property of equality

(3) $\displaystyle US=US$ Reflexive property of equality

(4) $\displaystyle TU+US=SV+US$ Addition property

(5) $\displaystyle TU+US=ST \ \ and \ \ SV+US=UV$ Segment addition postulate

(6) $\displaystyle ST=UV$ Substitution (4) and (5)