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

Angle 4 and 5 are  alternate interior angles.

The answer is: Alternate Interior Angles Theorem

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

Step-by-step 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.

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step-by-step explanation: