Question

Which statement needs to be true to prove that ∠1 is parallel to ∠3 (∠1 || ∠3)?

A) ∠1 + ∠3 = 180°
B) ∠1 - ∠2
C) ∠1 = ∠3
D) ∠1 = ∠4

Answer 1

To prove that angle ∠1 is parallel to angle ∠3, we can use the Alternate Interior Angles Theorem. If ∠1 = ∠3, according to the theorem, the lines are parallel. Therefore, the correct statement is ∠1 = ∠3 (option C).

Step-by-step explanation:

To prove that angles ∠1 (∠1) is parallel to angle ∠3 (∠3), there are certain postulates and theorems from geometry that can be applied. If ∠1 and ∠3 are alternate interior angles formed by a transversal intersecting two lines, and they are equal, then the lines are parallel. Knowing that ∠1 = ∠3 helps us to directly apply the Alternate Interior Angles Theorem which states that if a transversal cuts two lines and the alternate interior angles are congruent, then the lines are parallel. Therefore, the statement that needs to be true is ∠1 = ∠3, which corresponds to option C. It's also important to note that according to the question the angle symbols might be inadvertently replaced by '∠', so reading it as 'angle' would be correct in the context of geometry.