Answer:
7.By transitive property of equality
8.By substitution property
9.Subtraction property of equality
10.Converse of angles congruence postulate.
Step-by-step explanation:
We are given that
[tex]\angle 2\cong \angle 4[/tex] , angle 2 and angle 3 are supplementary and angle 1 and angle 4 are supplementary.
We have to prove that [tex]\angle 1\cong\angle 3[/tex]
We have to write missing statements in given proof.
1.[tex]\angle 2\cong\angle 4[/tex]
Given
2.[tex]m\angle 2=m\angle 4[/tex]
Angle congruence postulate
3.Angle 2 and angle 3 are supplementary.
Given
4.[tex]m\angle 2+m\angle 3=180^{\circ}[/tex]
By definition of supplementary angles
5.Angle 1 and angle 4 are supplementary
Given
6.[tex]m\angle 1+m\angle 4=180^{\circ}[/tex]
By definition of supplementary angles
7.[tex]m\angle 1+m\angle 4=m\angle 2+m\angle 3[/tex]
By transitive property of equality
8.[tex]m\angle 1+m\angle 4=m\angle 4+m\angle 3[/tex]
By substitution property
9.[tex]m\angle 1=m\angle 3[/tex]
Subtraction property of equality
10.[tex]m\angle 1\cong m\angle 3[/tex]
Converse of angle congruence postulate
