To solve for the missing steps, let's rewrite first the problem.
Given:
In a plane, line m is perpendicular to line t or m⟂t
line n is perpendicular to line t or n⟂t
Required:
Prove that line m and n are parallel lines
Solution:
We know that line t is the transversal of the lines m and n.
With reference to the figure above,
∠ 2 and ∠ 6 are right angles by definition of perpendicular lines. This states that if two lines are perpendicular with each other, they intersect at right angles.
So ∠ 2 ≅ ∠ 6. Since corresponding angles are congruent.
Therefore, line m and line n are parallel lines.
ANSWERS: perpendicular lines, corresponding