Answer: 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
