select the correct answer from each drop - down menu.\nin the figure below, u || v.\nprove: ∠3 and ∠5 are…

select the correct answer from each drop - down menu.\nin the figure below, u || v.\nprove: ∠3 and ∠5 are congruent.\nstatements reasons\n1. u || v given\n2. ∠1 ≅ ∠7 \n3. ∠5 ≅ ∠7 vertical angles theorem\n4. ∠1 ≅ ∠3 vertical angles theorem\n5. ∠3 ≅ ∠5

select the correct answer from each drop - down menu.\nin the figure below, u || v.\nprove: ∠3 and ∠5 are congruent.\nstatements reasons\n1. u || v given\n2. ∠1 ≅ ∠7 \n3. ∠5 ≅ ∠7 vertical angles theorem\n4. ∠1 ≅ ∠3 vertical angles theorem\n5. ∠3 ≅ ∠5

Answer

Answer:

  1. Reasons: alternate - exterior angles theorem
  2. Reasons: transitive property of congruence

Explanation:

Step1: Identify reason for ∠1≅∠7

When two parallel lines u and v are cut by a transversal, ∠1 and ∠7 are alternate - exterior angles. By the alternate - exterior angles theorem, alternate - exterior angles are congruent when the lines are parallel.

Step2: Identify reason for ∠3≅∠5

We know that ∠1≅∠7, ∠1≅∠3 and ∠5≅∠7. Since congruence is transitive (if a = b and b = c, then a = c), for angles, if ∠1≅∠7 and ∠1≅∠3 and ∠5≅∠7, then ∠3≅∠5 by the transitive property of congruence.