The given theorem is the proof of the vertical angles theorem.
What is the vertical angle theorem?
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 the vertical angles theorem.
The complete question is given below with the image attached.
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. which type of theorem is this?
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