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Geometry chapter 6 Polygons
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Terms in this set (39)
Polygon interior angle sum theorem
(n-2)180
Polygon exterior angle theorem
360
regular polygon
always convex, equilateral, equiangular
convex polygon
all diagonals fall inside the polygon
concave polygon
not all diagonals fall inside the polgon
definition of a parallelogram
a quadrilateral with two pairs of parallel sides
6-2 if a quadrilateral is a parallelogram
then opposite sides
then opposite sides are congruent.
if a quadrilateral is a parallelogram
opposite angles are
then opposite angles are congruent
if a quadrilateral is a parallelogram
consecutive angles are
then consecutive angles are supplementary
if a quadrilateral is a parallelogram
diagonals
then its diagonals bisect each other
6-3 A quadrilateral with one pair of opposite sides are parallel and congruent then
it is a parallelogram
A quadrilateral with opposite sides congruent is a
parallelogram
A quadrilateral with opposite angles congruent is a
parallelogram
A quadrilateral with an angle supplementary to both consecutive angles then it is a
parallelogram
if the diagonals bisect each other in a quadrilateral then it is a
parallelogram
6-4 if a quadrilateral is a rectangle then it is a
parallelogram
If a parallelogram is a rectangle then
its angles are congruent
If a quadrilateral is a rhombus then
it is a parallelogram
If a parallelogram is a rhombus then
its diagonals are perpendicular
If a parallelogram is a rhombus then
each diagonal bisects a pair of opposite angles
A rectangle is
a quadrilateral with 4 right angles
A rhombus is
a quadrilateral with 4 congruent sides
A square is
a quadrilateral with 4 right angles and 4 congruent sides
6-5 If one angle of a parallelogram is a right angle then it is
a rectangle
If the diagonals of a parallelogram are congruent then it is
a rectangle
If one pair of consecutive sides of a parallelogram are congruent then it is
a rhombus
if the diagonals of a parallelogram are perpendicular then it is a
rhombus
if one diagonal bisects a pair of opposite angles then the parallelogram is
a rhombus
6-6 If a Quadrilateral is a kite, then its diagonals are
perpendicular
If a Quadrilateral is a kite, then exactly one pair
of opposite angles are congruent
A kite definition
is a quadrilateral with exactly two pairs of congruent consecutive sides
Definition of trapezoid
a quadrilateral with exactly one pair of parallel sides,
parallel sides are the bases,
nonparallel sides are the legs
Base angles of a trapezoid
two consecutive angles whose common side is a base.
isosceles trapezoid
trapezoid whose legs are congruent
If a quadrilateral is a trapezoid then each pair of base angles
are congruent
If a trapezoid has one pair of congurent base angles
then it is isosceles
If a trapezoid is isoceles if and only if
its diagonals are congurent
midsegment of a trapezoid
the segment whose endpoints are the midpoints of the legs.
trapezoid midsegment theorem
the midsegment is parallel to each base, and its length is one half the sum of the lenghts of the bases. 1/2(ab+cd)
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