# Parallel And Perpendicular Lines Worksheet Page 43

Geometry Activity
Geometry Activity
Every great circle of a sphere intersects all other great circles on that sphere
in exactly two points. In the figure at the right, one possible line through
Q
point A intersects line
at P and Q.
A
If two great circles divide a sphere into four congruent regions, the lines
are perpendicular to each other at their intersection points. Each longitude
P
circle on Earth intersects the equator at right angles.
Compare Plane and Spherical Geometries
For each property listed from plane Euclidean geometry, write a corresponding
statement for spherical geometry.
a. Perpendicular lines intersect at one point.
b. Perpendicular lines form four right angles.
x
m
y
P
Perpendicular great circles intersect at
Perpendicular great circles form eight
two points.
right angles.
x
P
y
m
Q
Exercises
For each property from plane Euclidean geometry, write a corresponding
statement for spherical geometry.
A line goes on infinitely in two directions.
1.
A line segment is the shortest path between two points.
2.
Two distinct lines with no point of intersection are parallel.
3.
Two distinct intersecting lines intersect in exactly one point.
4.
A pair of perpendicular straight lines divides the plane into four infinite regions.
5.
Parallel lines have infinitely many common perpendicular lines.
6.
7.
There is only one distance that can be measured between two points.
If spherical points are restricted to be nonpolar points, determine if each
statement from plane Euclidean geometry is also true in spherical geometry.
Any two distinct points determine exactly one line.
8.
9.
If three points are collinear, exactly one point is between the other two.
Given a line and point P not on , there exists exactly one line parallel to
10.
passing through P.
166 Investigating Slope-Intercept Form
166 Chapter 3 Parallel and Perpendicular Lines