Question

10.) select which goes in the corresponding space reason (5) * 5 points given: <1 & <2, <3 & <4 are supplements. <1 == <4 prove: <2 == <3 statements reasons 1) <1 & <2, <3 & <4 are 1) given supplements and <1 ~= <4 2) definition of supplementary 2) m<1+m<2=180 angles m<3+m<4=180 3) definition of congruence 3) m<1=m<4 4) m<1+m<2=m<3+m<4 4) 5)m<1+m<2=m<3+m<1 5) 6)m<2=m<3 6) 7)<2~=<3 7) definition of congruency subtraction property of equality substitution property of equality definition of supplementary angles transitive property of equality

Explanation:

Step1: Analyze step 4

In step 4, we have $m\angle1 + m\angle2=m\angle3 + m\angle4$. In step 5, we have $m\angle1 + m\angle2=m\angle3 + m\angle1$. Since we know from step 3 that $m\angle1=m\angle4$, we are substituting $m\angle4$ with $m\angle1$.

Step2: Recall property

The property that allows us to replace one quantity with an equal - valued quantity is the Substitution Property of Equality.

Answer:

Substitution Property of Equality