Question

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Drag and drop the correct answer into each box to complete the proof.

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° 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 __________

∠N≅∠L and ∠M≅∠K ________

Options:

1. Corresponding Angles Postulate

2. Subtraction Property of Equality

3. Angle Congruence Postulate

4. Definition of congruence

Answer 1

Same Side Interior Angles  Theorem
Subtraction Property of Equality
Angle Congruence Postulate 

Answer 2

Consider the given parallelogram KLMN.

Prove: $\angle N \cong \angle L, \angle K \cong \angle M$

 Statement                                                                       Reason

1. $KL \parallel NM, KN \parallel LM$               Definition of parallelogram

2. $\angle K+ \angle N = 180^\circ$                 Same Side interior angle theorem

   $\angle L+ \angle M = 180^\circ$

  $\angle K+ \angle L = 180^\circ$

3. $\angle K+ \angle N=\angle K+ \angle L$   Substitution property

  $\angle L+ \angle M=\angle K+ \angle L$

4. $\angle N = \angle L$                                 Subtraction property of equality

  $\angle M = \angle K$

Subtraction property of equality tells us that if we subtract some number from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

5.  $\angle N \cong \angle L$                         Angle Congruence Postulate

  $\angle M \cong \angle K$

When two angles are equal, then they are said to be congruent by Angle congruence postulate.