Question

1. complete the statements regarding mathematical properties.

the statement, (mangle abc = mangle abc) demonstrates the __ choice 1 __.
the statement, if (angle rtycong oiu), then (angle oiucong rty) demonstrates the __ choice 2 __.
the statement, if (mangle mjn + mangle cvb=252^{circ}) and (mangle mjn = 76^{circ}), then (76^{circ}+mangle cvb = 252^{circ}) demonstrates the __ choice 3 __.
the statement, if (angle yhncongangle tgb) and (angle tgbcongangle rfv), then (angle yhncongangle rfv) demonstrates the __ choice 4 __.
the statement, if (mangle dwq = mangle cxz) and (mangle cxz = 16^{circ}), then (mangle dwq = 16^{circ}) demonstrates the __ choice 5 __.
choice 1:

1. reflexive property of equality 2. reflexive property of congruence 3. substitution property of equality
2. symmetric property of congruence 5. transitive property of equality

choice 2:

1. reflexive property of equality 2. substitution property of equality
2. substitution property of congruence 4. symmetric property of congruence
3. transitive property of congruence

choice 3:

1. substitution property of equality 2. substitution property of congruence
2. symmetric property of equality 4. symmetric property of congruence 5. transitive property of equality

choice 4:

1. reflexive property of equality 2. reflexive property of congruence
2. symmetric property of congruence 4. transitive property of equality
3. transitive property of congruence

choice 5:

1. reflexive property of equality 2. substitution property of congruence
2. symmetric property of equality 4. transitive property of equality 5. transitive property of congruence

Explanation:

Step1: Analyze first statement

The statement $m\angle ABC = m\angle ABC$ shows a quantity equal to itself, which is the reflexive property of equality.

Step2: Analyze second statement

The statement if $\angle RTY\cong OIU$, then $\angle OIU\cong RTY$ shows that congruence can be reversed, which is the symmetric property of congruence.

Step3: Analyze third statement

Given $m\angle MJN + m\angle CVB=252^{\circ}$ and $m\angle MJN = 76^{\circ}$, substituting $76^{\circ}$ for $m\angle MJN$ in the first - equation is the substitution property of equality.

Step4: Analyze fourth statement

The statement if $\angle YHN\cong\angle TGB$ and $\angle TGB\cong\angle RFV$, then $\angle YHN\cong\angle RFV$ shows that if two angles are congruent to a third angle, they are congruent to each other, which is the transitive property of congruence.

Step5: Analyze fifth statement

The statement if $m\angle DWQ = m\angle CXZ$ and $m\angle CXZ = 16^{\circ}$, then $m\angle DWQ = 16^{\circ}$ shows that if two quantities are equal to a third quantity, they are equal to each other, which is the transitive property of equality.

Answer:

Choice 1: 1. Reflexive Property of Equality
Choice 2: 4. Symmetric Property of Congruence
Choice 3: 1. Substitution Property of Equality
Choice 4: 5. Transitive Property of Congruence
Choice 5: 4. Transitive Property of Equality