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The reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
So, extend segments JM and JK beyond points M and J, respectively, and draw points P and Q.
It is assumed that a parallelogram with segments JM parallel to segments KL and JK parallel to segments ML is presented.
Draw point P and extend segment JM past point M through construction.
Through construction also Continue segment JK draws point Q after point J.
Consequently, the Alternate Interior Angles Theorem ∠MLK≅∠PML and ∠JML≅∠QJM (1)
Then, the corresponding angles theorem ∠PML≅∠KJM and ∠QJM≅∠LKJ is applied (2)
Equations (1) and (2) and the transitive property of equality are used to create:
∠MLK≅∠KJM and ∠JML≅∠LKJ
As a result, the supplied parallelogram JKLM's opposite angles are congruent. So it was proved.
Therefore, the reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
Know more about a parallelogram here:
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Correct 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 1. 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, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. 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?
a. Alternate Interior Angles Theorem
b. Corresponding Angles Theorem
c. Same-Side Interior Angles Theorem
d. Same-Side Interior Angles Theorem
