Question

complete the statements regarding mathematical properties
the statement m∠abc = m∠abc demonstrates the
the statement, if ∠rty ≅ ∠oiu, then ∠oiu ≅ ∠rty demonstrates the
the statement, if m∠mjn + m∠cvb = 252° and m∠mjn = 76°, then 76° + m∠cvb = 252° demonstrates the
the statement, if ∠yhn ≅ ∠tgb and ∠tgb ≅ ∠rfv, then ∠yhn ≅ ∠rfv demonstrates the
the statement, if m∠dwq = m∠cxz and m∠cxz = 16°, then m∠dwq = 16° demonstrates the

Explanation:

Step1: Identify property for \(m\angle ABC=m\angle ABC\)

This is the reflexive property as any quantity is equal to itself.

Step2: Identify property for if \(\angle RTY\cong\angle OIU\), then \(\angle OIU\cong\angle RTY\)

This is the symmetric property of congruence which states that if \(A\cong B\), then \(B\cong A\).

Step3: Identify property for if \(m\angle MJN + m\angle CVB=252^{\circ}\) and \(m\angle MJN = 76^{\circ}\), then \(76^{\circ}+m\angle CVB = 252^{\circ}\)

This is the substitution property where we substitute the value of \(m\angle MJN\) into the equation.

Step4: Identify property for if \(\angle YHN\cong\angle TGB\) and \(\angle TGB\cong\angle RFV\), then \(\angle YHN\cong\angle RFV\)

This is the transitive property of congruence which says that if \(A\cong B\) and \(B\cong C\), then \(A\cong C\).

Step5: Identify property for if \(m\angle DWQ=m\angle CXZ\) and \(m\angle CXZ = 16^{\circ}\), then \(m\angle DWQ = 16^{\circ}\)

This is the substitution property as we substitute the value of \(m\angle CXZ\) for \(m\angle DWQ\).

Answer:

1. Reflexive property
2. Symmetric property of congruence
3. Substitution property
4. Transitive property of congruence
5. Substitution property