Unit 5 - Polygons
Theorem/Postulate/Formula
Name and/or Number
Theorem 6.1 Polygon Interior Angles
Theorem
Actual Wording
The sum of the measures of the interior
)
angles of a convex n-gon is (
Corollary to Theorem 6.1
The measure of each interior angle of a
regular n-gon is (
)(
)
Theorem 6.2 Polygon Exterior Angles
Theorem
The sum of the measures of the exterior
angles, one from each vertex, of a convex
polygon is
Corollary to Theorem 6.2
The measure of each exterior angle of a
regular n-gon is (
)
Properties of Parallelograms
Theorem 6.3
If a quadrilateral is a parallelogram, then
its opposite sides are congruent.
Properties of Parallelograms
Theorem 6.4
If a quadrilateral is a parallelogram, then
its opposite angles are congruent.
Properties of Parallelograms
Theorem 6.5
If a quadrilateral is a parallelogram, then
its consecutive angles are supplementary.
Theorem 6.6 Diagonals of a
Parallelogram
If a quadrilateral is a parallelogram, then
the diagonals bisect each other.
Theorem 6.7
If both pairs of opposite sides of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Diagram/Example
In Your Own Words
Theorem 6.8
If both pairs of opposite angles of a
quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6.9
If an angle of a quadrilateral is
supplementary to both consecutive angles
then the quadrilateral is a parallelogram.
Theorem 6.10
If the diagonals of a quadrilateral bisect
each other, then the quadrilateral is a
parallelogram.
Theorem 6.11
If one pair of opposite sides of a
quadrilateral are congruent and parallel,
then the quadrilateral is a parallelogram.
Theorem 6.12
A parallelogram is a rhombus if and only if
its diagonals are perpendicular.
Theorem 6.13
A parallelogram is a rhombus if and only if
each diagonal bisects a pair of opposite
angles.
Theorem 6.14
A parallelogram is a rectangle if and only if
its diagonals are congruent.
Theorem 6.15
A quadrilateral is a rhombus if and only if
it has four congruent sides.
Theorem 6.16
A quadrilateral is a rectangle if and only if
it has four right angles.
Theorem 6.17 Trapezoid Base Angles
Theorem
If a trapezoid is isosceles, then each pair of
base angles are congruent.
Theorem 6.18 Trapezoid Diagonals
Theorem
If a trapezoid is isosceles, then its
diagonals are congruent.
Theorem 6.19
If a trapezoid has one pair of congruent
base angles, then it is an isosceles
trapezoid.
Theorem 6.20
If a trapezoid has congruent diagonals,
then it is an isosceles trapezoid.
Theorem 6.21 Midsegment Theorem
for Trapezoids
The midsegment of a trapezoid is parallel
to each base, and its length is half the sum
of the bases.
Theorem 6.22 SASAS Congruence
Theorem
If three sides and the included angles of
one quadrilateral are congruent to the
corresponding three sides and included
angles of another quadrilateral, then the
quadrilaterals are congruent.
Theorem 6.23 ASASA Congruence
Theorem
If three angles and the included sides of
one quadrilateral are congruent to the
corresponding three angles and included
sides of another quadrilateral, then the
quadrilaterals are congruent.
Theorem 6.24
If a quadrilateral is a kite, then its
diagonals are perpendicular.
Theorem 6.25
If a quadrilateral is a kite, then exactly one
pair of opposite angles are congruent.