Question

. Complete the missing steps in the paragraph proof of Theorem 3-8.

Answer 1

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