Question

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 N Given: Parallelogram KLMN Prove: ∠N≅∠L and ∠M≅∠K

Answer 1

Opposite angles of a parallelogram are congruent.

Explanation:

Given:

KLMN is a parallelogram.

KN ║ LM and KL ║MN.

To prove:

∠N ≅ ∠L

∠M ≅ ∠K

Proof:

∠N ≅ ∠L since the opposite angles of a parallelogram are congruent.

∠M ≅ ∠K since the opposite angles of a parallelogram are congruent.

Answer 2

Answer: Parallelogram KLMN Given

KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and Kn---------llLM Definition of parallelogram

m∠K+m∠N=180°

m∠L+m∠M=180°

m∠K+m∠L=180° Same-Side Interior Angles Theorem

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 Subtraction Property of Equality

∠N≅∠L

and ∠M≅∠K

Angle Congruence Postulate

Explanation:

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