Question

1. given 2 parallel lines and a transversal that intersects both parallel lines, what must be true about the pairs of corresponding angles?

a. the angles must be congruent.
b. the angles must be complementary.
c. the angles must be supplementary.
d. the angles must be obtuse.

1. determine whether the lines are parallel, perpendicular, or neither:

$y = 2x + 5$
$y = - 2x - 3$
a. parallel
b. perpendicular
c. neither

Explanation:

Question 11

When two parallel lines are cut by a transversal, the corresponding angles are congruent. Complementary angles add up to \(90^{\circ}\), supplementary angles add up to \(180^{\circ}\), and there is no requirement for corresponding angles to be obtuse (angles greater than \(90^{\circ}\) but less than \(180^{\circ}\)).

For two lines \(y = m_1x + b_1\) and \(y=m_2x + b_2\), if \(m_1=m_2\), the lines are parallel. If \(m_1\times m_2=- 1\), the lines are perpendicular. Here, \(m_1 = 2\) and \(m_2=-2\). Since \(2
eq - 2\) (not parallel) and \(2\times(-2)=-4
eq - 1\) (not perpendicular).

Answer:

A. The angles must be congruent.

Question 12