Proving Vertical Angles Are Congruent

Question

Given: Angle 2 and angle 4 are vertical angles

Prove: angle 2 is congruent to angle 4

Statement options:

1. m angle 2+ m angle 3= 180
2. m angle 3+ m angle 4= 180
3. angle 2 and angle 3 are a linear pair
4. angle 3 and angle 4 are a linear pair
5. m angle 2+ m angle 3= m angle 3+ m angle 4
6. lines m and n intersect at P

Reason Options:

1. def. of a linear pair
2. def. of vertical angles
3. substitution property
4. angle addition postulate

Answer 1

Thoroughly confusing

Given that angle 2 and angle 4 are vertical angles, then there is an angle between them,

looks like angle 3 , so that angle 2 and angle 3 are linear pairs and angle 3 and angle 4 are

linear pairs. So then angle 2 + angle 3 = angle 3 + angle 4 = 180

Subtracting angle 3 from both sides proves the theorem...

Statement Reason

Angle 2 and Angle 3 are vertical angles given

Angle 2 and Angle 3 are linear pairs AND definition/construction of vertical angles

Angle 3 and Angle 4 are linear pairs

Linear pairs are supplementary definition of linear pairs

Angle 2 + Angle 3 = 180 and supplementary angles must total 180 degrees

Angle 3 + Angle 4 = 180

Angle 2+ Angle3 = Angle 3 + angle 4 substitution/transitive

Angle 2 = Angle 4 subtraction property of equality