Question

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:

Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML.

Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 2. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, numbered blank 1. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, Corresponding Angles Theorem. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.

Which reasons can be used to fill in the numbered blank spaces?

Alternate Interior Angles Theorem
Corresponding Angles Theorem

Corresponding Angles Theorem
Alternate Interior Angles Theorem

Alternate Interior Angles Theorem
Same-Side Interior Angles Theorem

Corresponding Angles Theorem
Same-Side Interior Angles Theorem

Answer 1

@563blackghost

Answer 2

@Hero @Shadow