Question

1. write the conclusion for the statement. if m∠jkl + m∠smw = m∠xyz + m∠dnf and m∠xyz = m∠smw, then... 8. name the property to justify the statement in question 7. complete the proof. 9. m∠mnp = m∠dfg 10. definition of congruence

Explanation:

Step1: Substitute equal - angle measures

Given \(m\angle JKL + m\angle SMW=m\angle XYZ + m\angle DNF\) and \(m\angle XYZ = m\angle SMW\). Substitute \(m\angle XYZ\) with \(m\angle SMW\) in the first equation: \(m\angle JKL + m\angle SMW=m\angle SMW + m\angle DNF\).

Step2: Subtract \(m\angle SMW\) from both sides

Using the subtraction property of equality, \((m\angle JKL + m\angle SMW)-m\angle SMW=(m\angle SMW + m\angle DNF)-m\angle SMW\), which simplifies to \(m\angle JKL=m\angle DNF\).

For question 8:
The property used in question 7 is the Subtraction Property of Equality.

For question 9:
The reason could be "Given" (since no other information is provided about how we know \(m\angle MNP = m\angle DFG\)).

For question 10:
If the reason is the definition of congruence, the statement could be \(\angle MNP\cong\angle DFG\) (because the definition of congruence for angles states that if the measures of two angles are equal, the angles are congruent).

Answer:

1. \(m\angle JKL=m\angle DNF\)
2. Subtraction Property of Equality
3. Reason: Given
4. Statement: \(\angle MNP\cong\angle DFG\)