Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.
What are parallel lines?
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.
In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.
Based on these reasons, we can prove the following statements:
m || n (given)
m∠1 ≅ m∠7 (alternate exterior angle theorem).
m∠7 ≅ m∠5 (vertical angles theorem).
m∠1 ≅ m∠7 (transitive property of congruence).
In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.
