Chapter 6 – Analytic
6-1 Coordinate Proofs
1. To prove theorems from geometry by
What is Analytic Geometry?
study of geometric problems
using algebraic methods.
◦ Distance Formula
◦ Midpoint Formula
Placing Coordinate Axes
For a right triangle, axes should be
placed so the legs lie on them
want a parallel side on the x-axis
and a vertex at the origin
How to Construct a
and label a coordinate diagram
List given information
State what you will prove
Use given info to add to the diagram
Use algebra to prove statement
◦ “Therefore, blah = blah.”
Common Methods to use:
Segments are equal use distance
Lines are parallel show slopes are
Lines are perpendicular show slopes
multiply to -1
Segments bisect show they have the
Lines are concurrent show equations
have a common solution
that the midpoint of the
hypotenuse of a right triangle is
equidistant from the three vertices.
that the median of a trapezoid
is parallel to the bases and has
length equal to the average length
of the bases.
that the altitudes of a triangle
are concurrent (meet at one point).