Examine the paragraph proof. which theorem does it offer proof for?

lines wz and xy intersect at point v

prove: ∠xvz ≅ ∠wvy

we are given an image of line wz and line xy, which intersect at point v. m∠xvz + m∠zvy = 180° by the definition of supplementary angles. m∠zvy + m∠wvy = 180° by the definition of supplementary angles. since the sum of m∠xvz + m∠zvy = m∠zvy + m∠wvy by the transitive property of equality, m∠zvy can be subtracted from both sides of the equation because of the subtraction property of equality. therefore, m∠xvz = m∠wvy and ∠xvz ≅ ∠wvy by the definition of congruent angles.