Question

Lines m and n are parallel. Which Postulate or Theorem proves that <4 ≅ <5?

Image result for parallel lines cut by a transversal
Question 12 options:


Corresponding Angles Postulate


Alternate Interior Angles Theorem


Vertical Angles Theorem


Alternate Exterior Angles Theorem

Answer 1

The correct option is 2. ∠4≅∠5 by using alternate interior angles theorem.

Explanation:

Corresponding Angles Postulate: If a transversal line intersect two parallel lines, then the corresponding angles are congruent.

Alternate Interior Angles Theorem: If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

Vertical Angles Theorem: If two lines intersect each other, then vertically opposite angles are congruent.

Alternate Exterior Angles Theorem: If a transversal line intersect two parallel lines, then the alternate exterior angles are congruent.

From the given figure it is clear that the m║n, t is transversal line, ∠4 and ∠5 are alternate interior angles.

∠4≅∠5 (By using alternate interior angles theorem)

Therefore the correct option is 2.

Answer 2

Angle 4 and 5 are alternate interior angles.

The answer is: Alternate Interior Angles Theorem