"Angle 1 and angle 2 are supplementary. Angle 3 and 4 are supplementary. Angle 2 is congruent to angle 3. Prove angle 1 is congruent to angle 4

Question

 "Angle 1 and angle 2 are supplementary. Angle 3 and 4 are supplementary. Angle 2 is congruent to angle 3. Prove angle 1 is congruent to angle 4"

Answer 1

1)  Angle 1 and angle 2 are supplementary; ∴ angle1 + angle2=180^o

2)  Angles 3 and 4 are supplementary; ∴ angle3 + angle4 = 180^o

3)  Angle2 is congruent to angle 3; ∴ angle2 = angle3

4)  Angle1 + angle2 - angle3 - angle4 = 0 by subtraction, statement 1) minus statement 2).

5) Because of statement 3, angle 2 - angle 3 = 0.

6) Substituting the above 0 for the middle part of statement 4, we get angle1 - angle4 = 0

7) Statement 7) is equivalent to angle1 = angle 4. QED.