Question

4 multiple choice 1 point the corresponding angles conjecture states that if two parallel lines are cut by a transversal, the alternate interior angles are congruent. the picture below shows this relationship. to test this conjecture, which pair of congruent angles are alternate interior angles? ∠4 and ∠8 ∠3 and ∠5 ∠2 and ∠8 ∠1 and ∠4 5 multiple choice 1 point what is the slope of all lines perpendicular to the line 2x + 3y = 6? 3/2 -1/2 -2/3 2/3

Explanation:

Question 4

Alternate interior angles are non - adjacent angles that lie between two parallel lines and on opposite sides of a transversal.

• For \(\angle4\) and \(\angle8\), \(\angle4\) is between the parallel lines \(l\) and \(m\) and \(\angle8\) is not between the parallel lines \(l\) and \(m\) (it is below line \(m\)).
• For \(\angle3\) and \(\angle5\), \(\angle3\) and \(\angle5\) are non - adjacent, lie between the parallel lines \(l\) and \(m\), and are on opposite sides of the transversal.
• For \(\angle2\) and \(\angle8\), \(\angle2\) is above line \(l\) and \(\angle8\) is below line \(m\), so they are not alternate interior angles.
• For \(\angle1\) and \(\angle4\), \(\angle1\) and \(\angle4\) are adjacent (they share a common side), so they are not alternate interior angles.

Step1: Convert the given line to slope - intercept form \(y = mx + b\)

The given line is \(2x+3y = 6\).
Subtract \(2x\) from both sides: \(3y=-2x + 6\).
Divide each term by \(3\): \(y=-\frac{2}{3}x+2\). The slope of the line \(2x + 3y=6\) is \(m_1=-\frac{2}{3}\).

Step2: Use the formula for the slope of a perpendicular line

If two lines with slopes \(m_1\) and \(m_2\) are perpendicular, then \(m_1\times m_2=- 1\).
Let \(m_1 =-\frac{2}{3}\), and we want to find \(m_2\).
We have \(-\frac{2}{3}\times m_2=-1\).
Solve for \(m_2\): \(m_2=\frac{-1}{-\frac{2}{3}}=\frac{3}{2}\)

Answer:

\(\angle3\) and \(\angle5\)

Question 5