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parallelogram K L M N where K N is parallel to L M and K L is parallel to M N

Given: Parallelogram KLMN

Prove: ∠N≅∠L and ∠M≅∠K Statement Reason
Parallelogram KLMN Given
KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and KN¯¯¯¯¯¯∥LM¯¯¯¯¯¯ Definition of parallelogram
m∠K+m∠N=180°

m∠L+m∠M=180°

m∠K+m∠L=180°

Response area
m∠K+m∠N=m∠K+m∠L

m∠L+m∠M=m∠K+m∠L

Substitution Property of Equality
m∠N=m∠L

m∠M=m∠K

Response area
∠N≅∠L and ∠M≅∠K