Question

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

Answer 1

Answer:∠JML ≅ ∠QJM

Alternate Interior Angles Theorem      

Step-by-step explanation:

Here, Given: JKML is a parallelogram,

That is, JK ║ ML and JM ║ KL

Prove: ∠ MLK ≅ ∠ KJM and ∠ JML ≅ ∠ LKJ

Extend segment JM beyond point  and draw point P (Construction)

∠ MLK ≅ ∠ PML                           ( Alternate Interior Angles Theorem)

∠ PML ≅ ∠KJM                             (  Corresponding Angles Theorem )

⇒ ∠ MLK ≅ ∠ KJM                        ( By transitive property of equality )

Extend segment JK beyond point J and draw point Q, by Construction.

∠JML ≅ ∠QJM                              ( Alternate Interior Angles Theorem)

∠ QJM ≅ ∠ LKJ                            (  Corresponding Angles Theorem )

⇒ ∠JML ≅ ∠ LKJ                          ( By transitive property of equality )

Thus, the opposite angles of parallelogram JKLM are congruent.