11) Complete the two-column proof to prove the theorem: "If two lines are cut by a transversal where same side interior angles are supplementary, then the lines are parallel. (If SSIA supp, then \(\parallel\) lines.)"
Statements (Claims) |
Reasons (Evidence) |
\(\angle 3\) supp \(\angle 5\) |
\(\) |
\(\angle 3\) supp \(\angle 1\) |
\(\) |
\(m\angle 3 + m\angle 5 = 180^{\circ}\) |
\(\) |
\(m\angle 3 + m\angle 1 = 180^{\circ}\) |
\(\) |
\(m\angle 3 + m\angle 5 = m\angle 3 + m\angle 1\) |
\(\) |
\(m\angle 5 = m\angle 1\) |
\(\) |
\(\angle 5\cong\angle 1\) |
\(\) |
\(w\parallel s\) |
\(\) |
12) On the north part of Chicago, there are two diagonal streets, Milwaukee and Grand, that appear parallel. Using Pulaski as a transversal, we can use a protractor on the map to determine if Milwaukee and Grand are parallel streets or not. Examine the following chart. Are the parallel? Why or why not?
13) Are the sides of the John Hancock building in Chicago parallel? Use the cross beam and the measured angles and justify your answer.
14) Pictured below is a scissor lift. For the blue beams (lines) to be parallel, what would be the relationship between \(a^{\circ}\) and \(b^{\circ}\)? As the lift raises, what happens to the angles marked as \(a^{\circ}\) and \(b^{\circ}\)?