Question

question 11: examine the paragraph proof. which theorem does it offer proof for? prove: ∠xvz≅∠zwy. we are given an image of vz and xy, which intersect at point v. m∠xvz + m∠zvy = 180° by the definition of supplementary angles. m∠zvy + m∠zwy = 180° by the definition of supplementary angles. since the sum of m∠xvz + m∠zvy = m∠zvy + m∠zwy 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∠zwy and ∠xvz≅∠zwy by the definition of congruent angles. alternate interior angles theorem, corresponding angles theorem, vertical angles theorem, same - side interior angles theorem. question 12:

Explanation:

Step1: Recall supplementary - angle property

We know that if two angles are supplementary, their sum is 180°. Given that $\angle XYZ$ and $\angle ZYV$ are supplementary ($m\angle XYZ + m\angle ZYV=180^{\circ}$) and $\angle ZYV$ and $\angle WYV$ are supplementary ($m\angle ZYV + m\angle WYV = 180^{\circ}$).

Step2: Use the subtraction property of equality

Since $m\angle XYZ + m\angle ZYV=m\angle ZYV + m\angle WYV$, by the subtraction property of equality, we can subtract $m\angle ZYV$ from both sides of the equation. So, $m\angle XYZ=m\angle WYV$.

Step3: Recall the definition of congruent angles

If two angles have equal measures, they are congruent. Since $m\angle XYZ = m\angle WYV$, then $\angle XYZ\cong\angle WYV$ by the definition of congruent angles.

Answer:

The proof uses the Definition of Supplementary Angles and the Subtraction Property of Equality to show that $\angle XYZ\cong\angle WYV$.