Question

homework 2.5/2.6 - proving geometric relationships
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complete the statements regarding mathematical properties.
the statement (mangle abc=mangle abc) demonstrates the
the statement, if (angle rtycongangle oiu), then (angle oiucongangle rty) demonstrates the
the statement, if (mangle mjn + mangle cvb=252^{circ}) and (mangle mjn = 76^{circ}), then (76^{circ}+mangle cvb = 252^{circ}) demonstrates the
the statement, if (angle yhncongangle tgb) and (angle tgbcongangle rfv), then (angle yhncongangle rfv) demonstrates the
the statement, if (mangle dwq=mangle cxz) and (mangle cxz = 16^{circ}), then (mangle dwq = 16^{circ}) demonstrates the

Explanation:

Step1: Recall property definitions

The reflexive property states that a quantity is equal to itself. So, $m\angle ABC = m\angle ABC$ shows the reflexive property.

Step2: Recall symmetric property

The symmetric property of equality or congruence says that if $a=b$ (or $a\cong b$), then $b = a$ (or $b\cong a$). So, if $\angle RTY\cong\angle OIU$, then $\angle OIU\cong\angle RTY$ shows the symmetric property.

Step3: Recall substitution property

The substitution property allows us to replace a quantity with its equal. If $m\angle MJN + m\angle CVB=252^{\circ}$ and $m\angle MJN = 76^{\circ}$, then substituting $m\angle MJN$ with $76^{\circ}$ gives $76^{\circ}+m\angle CVB = 252^{\circ}$, which is the substitution property.

Step4: Recall transitive property

The transitive property states that if $a = b$ and $b = c$, then $a=c$ (or for congruence, if $a\cong b$ and $b\cong c$, then $a\cong c$). So, if $\angle YHN\cong\angle TGB$ and $\angle TGB\cong\angle RFV$, then $\angle YHN\cong\angle RFV$ shows the transitive property.

Step5: Recall substitution property again

If $m\angle DWQ=m\angle CXZ$ and $m\angle CXZ = 16^{\circ}$, substituting $m\angle CXZ$ with $16^{\circ}$ to get $m\angle DWQ = 16^{\circ}$ is the substitution property.

Answer:

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