Make a conjecture (hypothesis) about the measures of Corresponding Angles formed by parallel lines and a transversal - Explain Please

Question

Make a conjecture (hypothesis) about the measures of Corresponding Angles formed by parallel lines and a transversal

Answer 1

Conjecture: The corresponding angles are equal.

 

For parallel lines, the alternate interior angles are equal.  Let these angles

be ∠1 and ∠2, then ∠1 ≅ ∠2.

 

Let the corresponding angle of ∠1 be ∠3.  Now ∠2 and ∠3 form a vertical angle,

and vertical angles are equal, ∠2 ≅ ∠3.

 

Since ∠1 ≅ ∠2 and∠ 2 ≅ ∠3, then ∠1 ≅ ∠3.  This means that the corresponding angles

are equal.