6.3 If a quadrilateral is a
parallelogram, then its
opposite sides are
congruent.
6.4 If a quadrilateral is a parallelogram, then its
opposite angles are congruent.
6.5 If a quadrilateral is a
parallelogram, then its
consecutive angles are
supplementary.
6.6 If a parallelogram
has 1 right angle, then
it has 4 right angles.
6.7 If a quadrilateral
is a parallelogram,
then its diagonals
bisect each other.
6.8 If a quadrilateral is a
parallelogram, then each
diagonal separates the
parallelogram into two
congruent triangles.
6.9: If both pairs of opposite sides are congruent, then the
quadrilateral is a parallelogram.
6.10: If both pairs of opposite angles are congruent, then
the quadrilateral is a parallelogram.
6.11: If the diagonals bisect each other, then the
quadrilateral is a parallelogram.
6.12: If one pair of opposite sides is both parallel &
congruent, then the quadrilateral is a parallelogram.
How do we PROVE?
GIVEN: n-sided Polygon
PROVE: the SUM of the interior angle measures =
180(n-2)
Many proof methods…
http://www.qc.edu.hk/math/Junior%20Secondary/interior%20angle.htm
Polygon Exterior Angles Sum Theorem
(a.k.a. “The Spider Theorem”)
THEO REM 6.2: Polygon Exterior Angles Sum Theorem
GIVEN: n-sided Polygon
PROVE: the SUM of the exterior angle measures =
360
Algebraic Proof
• By the Supplement Theorem, the sum of
straight angles (linear pairs) at the vertices of a
convex n-gon is: SumLinearPairs  180n
• Sum of interior angles of a convex n-gon:
SumInteriorAngles  180(n  2)
• Therefore the sum of the exterior angles of a
convex polygon could be represented by:
SumExteriorAngles  SumLinearPairs  SumInteriorAngles
SumExteriorAngles  (180n)  180(n  2) 
SumExteriorAngles  180n  180n  360
SumExteriorAngles  360