Download Review Chapter 6 6.1 - 6.3

Review Chapter 6
6.1 - 6.3
Naming Polygons
# of
Type of
Sides Polygon
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
# of
Sides
8
Type of
Polygon
octagon
9
nonagon
10
decagon
12
dodecago
n
n-gon
n
Identifying Convex and Concave
A polygon is convex
if no line that
contains a side of
the polygon
contains a point in
the interior of the
polygon.
A polygon is that is
not convex is
Definitions:
A polygon is equilateral if all of its sides
are congruent.
A polygon is equiangular if all of its
interior angles are congruent.
A polygon is regular if it is both
equilateral and equiangular.
Theorem 6.1:
Polygon Angle-Sum Theorem
The sum of the measures of the interior
angles of an n-gon is (n-2)180.
If you draw a diagonal in
a polygon, you create
triangles. Using the
Triangle Sum Theorem
you can conclude that
the sum of the measures
of the interior angles of a
quadrilateral is
2(180)=360°.
Corollary to Polygon Angle-Sum Theorem
The measure of each of the interior angles of a
regular polygon is
(Where n is the number of sides.)
( n  2)180
n
Theorem 6.2
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles
of a polygon, one at each vertex, is 360 degrees.
Corollary to Polygon Angle-Sum
Theorem
The measure of each of the interior angles of a
( n  2)180
regular polygon is
n
(Where n is the number of sides.)
Theorem 6.2
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles
of a polygon, one at each vertex, is 360
degrees.
PARALLELOGRAM:
A quadrilateral
with both pairs of
opposite sides parallel.
Theorem 6.3:
If
a quadrilateral is a parallelogram, then
its opposite sides are congruent.
Theorem 6.4:
If
a quadrilateral is a parallelogram, then
its consecutive angles are supplementary.
Theorem 6.5:
If
a quadrilateral is a parallelogram, then
its opposite angles are congruent.
Theorem 6.6:
If
a quadrilateral is a parallelogram, then
its diagonals bisect each other.
Theorem 6.7
If three (or more) parallel lines cut off
congruent segments on one transversal,
then they cut off congruent segments
on every transversal.
If …
then…
Theorem 6.8
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6.9
If an angle of a quadrilateral is
supplementary to both of its
consecutive angles, then the
quadrilateral is a parallelogram.
+
= 180°
Theorem 6.10
If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6.11
If the diagonals of a quadrilateral bisect
each other, then the quadrilateral is a
parallelogram.
Theorem 6.12
If one pair of opposite sides of a
quadrilateral is both congruent and
parallel, then the quadrilateral is a
parallelogram.
Summary: Proving Quadrilaterals
are //grams






Show that both pairs of opposite sides are //.
Show that both pairs of opposite angles are congruent.
Show that both pairs of opposite sides are congruent.
Show that one angle is supplementary to both consecutive angles.
Show that the diagonals bisect each other.
Show that one pair of opposite sides is congruent and parallel.