Question

Given the statements:

Line m is parallel to line n
∠1 ≅ ∠3
∠3 ≅ ∠6
∠1 ≅ ∠6

What can you conclude?
a) Lines m and n intersect
b) Lines m and n are perpendicular
c) Lines m and n are parallel
d) Lines m and n form a triangle

Answer 1

The correct answer is that lines m and n are parallel, as evidenced by the congruent corresponding angles given in the statements.

Step-by-step explanation:

Based on the given statements, we can conclude that lines m and n are parallel to each other. This conclusion is drawn from the fact that angles 1 and 3 are congruent (∨1 ≅ ∨3), and angles 3 and 6 are also congruent (∨3 ≅ ∨6). Given the transitive property of congruence, if ∨1 ≅ ∨3 and ∨3 ≅ ∨6, then ∨1 must be congruent to ∨6 (∨1 ≅ ∨6). Since corresponding angles are congruent, this implies that the lines m and n, which these angles are associated with, do not intersect or form an angle with each other; hence, they are parallel. The correct answer is c) Lines m and n are parallel.