Question

given: x || y
w is a transversal of x and y.
prove: ∠4 ≅ ∠5
statements reasons

1. x || y 1. given
2. w is a transversal 2. given
3. ∠4 ≅ ∠1 3. a
4. ∠1 ≅ ∠5 4. b
5. ∠4 ≅ ∠5 5. c

complete the two - column proof
a
b
c
symmetric property
transitive property
definition of supplementary angles

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since ∠4 and ∠1 are vertical angles, ∠4≅∠1. So reason A is "vertical angles are congruent".

Step2: Identify corresponding - angle property

When two parallel lines are cut by a transversal, corresponding angles are congruent. Since x∥y and ∠1 and ∠5 are corresponding angles, ∠1≅∠5. So reason B is "corresponding angles postulate".

Step3: Use transitive property

The transitive property of congruence states that if a≅b and b≅c, then a≅c. Since ∠4≅∠1 and ∠1≅∠5, then ∠4≅∠5. So reason C is "transitive property".

Answer:

A. vertical angles are congruent
B. corresponding angles postulate
C. transitive property