Answer :
1.[tex]\angle 2+\angle 3=180^{\circ}[/tex]
2.Linear postulate
3.[tex]\angle 2+\angle 3=\angle 3+\angle 4[/tex]
4.Subtraction property of equality
Step-by-step explanation:
We are given that angle 1. angle 2, angle 3 and angle 4 formed by two intersecting segment.
We have to prove that angle 2 and angle 4 are congruent.
Proof:
Statement 1:[tex]\angle 1,\angle 2,\angle 3 [/tex] and [tex]\angle 4[/tex] formed by two intersecting lines.
Reason: Given
Statement 2:[tex]\angle 3[/tex] and [tex]\angle 4[/tex] forms linear pair
Reason:By definition of linear pair
Statement 3:[tex]\angle 2[/tex] and [tex] 3[/tex] forms linear pair
Reason: By definition of linear pair
Statement 4:[tex]\angle 2+\angl 3=180^{\circ}[/tex]
Reason: Linear pair postulate
Statement 5:[tex]\angel 3+\angle 4=180^{\circ}[/tex]
Reason: Linear pair postulate
Statement 6:[tex]\angle 2+\angle 3=\angle 3+\angle 4[/tex]
Reason: By substitution property of equlaity
Statement 7:[tex]\angle 2=\angle 4[/tex]
Reason: Subtraction property of equality
