Answer:
Statement 3:[tex]m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5[/tex].
Reason:Alternate Interior Angles Theorem
Step-by-step explanation:
We are given that a triangle ABC.
We have a proof that the sum of interior angle measures pf triangle ABC is [tex]180^{\circ}[/tex].
We have to find the missing steps in the given proof.
Statement 1 :Let points A,B and C form a triangle.
Reason: Given
Statement 2:[tex]$\overleftrightarrow{DE}$[/tex] is a line passing through B and parallel to [tex]\overline{AC}[/tex] with angles as labeled.
Reason: Definition a parallel line and labeling angles.
Statement 3:[tex]m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5[/tex].
Reason:Alternate Interior Angles Theorem
Statement 4:[tex]m\angle 1=m\angle 4 and m\angle 3=m\angle 5[/tex]
Reason: Congruent angles have same measures
Statement 5 [tex] m\angle 2+m\angle 4+m\angle =180^{\circ}[/tex]
Reason: Angle addition and definition of a straight angle
Statement 6: [ytex]m\angle 1+m\angle 2+m\angle 3=180^{\circ}[/tex]
Reason : By substitution
Hence proved.
