What is the missing reason for the 5th step in the proof below? Given: Line AE intersects RV at point N.
Prove: Vertical angles ZANR and ZVNE are congruent.
Å
N
STATEMENTS
Line AE intersects RV at point N.
m ANV + ZVNE - 180
MZANV - 180 - ZVNE
REASONS
Given statement
Definition of linear pair:
These two angles form a linear pair, so their
measures sum to 180 degrees
Subtraction:
m2VNE is subtracted from both sides of the
equation
Definition of linear pairs
These two angles also form a linear pair, so their
measures sum to 180 degrees
ZANV + MZANR - 180
(180 - MZVNE)+ZANR - 180
?
ZANR = m2 VNE
ZANR a ZVNE
Simplify:
Simplifying of the equation by subtracting 180 from
both sides and adding m ZVNE to both sides.
Definition of congruent angles
These angles have the same measure, so by
definition, they are congruent.
QED