91Ó°ÊÓ

WRITINGHow are the Alternate Interior Angles Theorem (Theorem 3.2\()\) and the Alternate Exterior Angles Theorem (Theorem 3.3) alike? How are they different?

The perpendicular bisector of a segment is the line that passes through the ________ of the segment at a ________ angle

VOCABULARY Two lines are cut by a transversal. Which angle pairs must be congruent for the lines to be parallel?

How are the slopes of perpendicular lines related?

In Exercises \(3-6,\) fiind the coordinates of point \(\mathrm{P}\) along the directed line segment \(\mathrm{AB}\) so that \(\mathrm{AP}\) to \(\mathrm{PB}\) is the given ratio. (See Example 1.) $$A(-3,2), B(5,-4) ; 2 \text { to } 6$$

CRITICAL THINKING it possible for consecutive interior angles to be congruent? Explain.

In Exercises \(17-20,\) write an equation of the line passing through point \(\mathrm{P}\) that is perpendicular to the given line. Graph the equations of the lines to check that they are perpendicular. (See Example 4.) $$P(-8,0), 3 x-5 y=6$$

THOUGHT PROVOKING The postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry, is it possible that a transversal intersects two parallel lines? Explain your reasoning.

Your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. Is your friend correct? Explain your reasoning

Write the converse of the conditional statement. Decide whether it is true or false. If two angles are vertical angles, then they are congruent.