Drag and drop the correct answer into each box to complete the proof. parallelogram k l m n where k n is parallel to l m and k l is parallel to m ngiven: parallelogram klmnprove: ∠n≅∠l and ∠m≅∠kstatement reasonparallelogram klmn givenkl¯¯¯¯¯∥nm¯¯¯¯¯¯¯ and kn¯¯¯¯¯¯∥lm¯¯¯¯¯¯ m∠k+m∠n=180°m∠l+m∠m=180°m∠k+m∠l=180 °same-side interior angles theoremm∠k+m∠n=m∠k+m∠lm∠l+m∠m=m∠k+m ∠lm∠n=m∠lm∠m=m∠k∠n≅∠l and ∠m≅∠k angle congruence postulate

 Statements reasons are,

In First blank - By the property of parallelogram

In second blank - transitive property of equality

In third blank - Subtraction property of equality

Step-by-step explanation:

Transitive property of equality states that if a = b and b=c then a =c

While, Subtraction property of equality states that  subtraction of a number from the each side of equation does not change the equality of the equation.

That is, If a = b then we can write, a- c = b-c

Here, Given: Parallelogram KLMN

And, the opposite sides of the parallelogram are congruent and equal.

Prove: ∠N≅∠L and ∠M≅∠K

            Statement                                        Reason

1. KL∥NM and KN∥LM                     1. By the property of parallelogram

2. m∠K+m∠N=180°                            2. Same-Side Interior Angles Theorem

m∠L+m∠M=180°

m∠K+m∠L=180°

3.m∠K+m∠N=m∠K+m∠L                3. Transitive property of equality

m∠L+m∠M=m∠K+m∠L

4.m∠N=m∠L                                     4. By subtraction property of

m∠M=m∠K                                         equality  

5.  ∠N≅∠L and ∠M≅∠K                  5. Angle Congruence Postulate