The following is an incomplete flowchart proving that the opposite angles of parallelogram jklm are congruent: [check the images provided below] which reasons can be used to fill in the numbered blank spaces? a. (1. alternate interior angles theorem (2. corresponding angles theorem b. (1. corresponding angles theorem (2. alternate interior angles theorem c. (1. alternate interior angles theorem (2. same-side interior angles theorem d. (1. corresponding angles theorem (2. same-side interior angles theorem

 A. 1. Alternate Interior Angles Theorem

2. Corresponding Angles Theorem

Step-by-step explanation:

Since, According to the Alternate Interior Angles Theorem, alternative interior angles made on the parallel lines by the same transversal is always congruent.

Also, According to the Corresponding Angles Theorem, corresponding angles made on the parallel lines by the same transversal is always congruent.

Here, we have a parallelogram JKLM in which We have to prove that: The opposite angles of parallelogram JKLM are congruent.

For parallelogram JKLM, LK ║ MJ and LM ║KJ

Also, LK=MJ and  LM=KJ

Extent JK beyond point J and draw point Q,  (construction)

∠JML≅∠QJM (  Alternate Interior Angles Theorem )

But, ∠QJM≅∠LKJ ( Corresponding Angles Theorem )

∠JML≅∠LKJ ( transitive property of equality)  (1)

Extent JM beyond point M and draw point P,  (construction)

∠MLK≅∠PML (  Alternate Interior Angles Theorem )

But, ∠PML≅∠KJM ( Corresponding Angles Theorem )

∠MLK≅∠KJM ( transitive property of equality)  (2)

Thus, From equation 1) and 2)

The opposite angles of parallelogram JKLM are congruent.

Answer A. 1. Alternate Interior Angles Theorem

                    2. Corresponding Angles Theorem

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answer: 1 and 3

step-by-step explanation: