Transitive Property of Congruence vs. Equality

Question

XWY and RTU are supplementary        Given

XWY + RTU=180 Definition of Supplementary Angles

RTU +UTW = 180  Angles forming a linear pair sum to 180

XWY + RTU = RTU +UTW    Transitive Property Of Equality

XWY= UTW Algebra

VX || SU   Converse Of Corresponding Angles

Question area in bold:

I am trying to determine whether to use the transitive property of equality vs. congruence. My understanding was that equality came from real numbers, measurements etc, whereas congruence was formed from angles, such as the proof given above. This proof is also an answer from an IXL question(Geometry D.6).

I believed it to be Transitive Property Of Congruence, given what I though was a solid understanding. ????

Answer 1

Angles are congruent, but their measures are equal. Since it's a sum, you're really talking about their measures and should use the notation m∠XWY + m∠RTU = m∠RTU + m∠UTW. Since the sums of the measures are equal, the Transitive Property of Equality applies.