theorems and stuff chapter 6 Flashcards
(20 cards)
polygon angle sum thm
the sum of the interior angle measures of a convex polygon with n sides is (n-2)180
polygon exterior angle sum thm
the sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360
if a quadrilateral is a parallelogram then…
- opposite sides are congruent
- opposite angles are congruent
- consecutive angles are supplementary
- diagonals bisect one another
if one pair of opposite sides of a quadrilateral are parallel and congruent then…
it is a parallelogram
if both pairs of opposite sides of a quadrilateral are congruent then….
it is a parallelogram
if both pairs of opposite angles of a quadrilateral are congruent then…
it is a parallelogram
if an angle of a quadrilateral is supplementary to both of its consecutive angles then…
it is a parallelogram
if the diagonals of a parallelogram bisect each other then…
it is a parallelogram
if a quadrilateral is a rectangle then….
it is a parallelogram
its diagonals are congruent
if a quadrilateral is a rhombus then…
it is a parallelogram
it is a parallelogram
its diagonals are perp
if a parallelogram is a rhombus then…
each diagonal bisects a pair of opposite angles
if one angle of a parallelogram is a right angle then…
the parallelogram is a rectangle
if the diagonals of a parallelogram are congruent, then…
the parallelogram is a rectangle
if one pair of consecutive sides of a parallelogram are congruent, then…
the parallelogram is a rhombus
if the diagonals of a parallelogram are perp then…
the parallelogram is a rhombus
if one diagonal of a parallelogram bisects a pair of opposite angles then…
the parallelogram is a rhombus
if a quadrilateral is a kite then…
its diagonals are perp
one pair of opposite angles are congruent
if a quadrilateral is an isosceles trapezoid then…
each pair of the base angles are congruent
a trapezoid is isosceles if and only if
its diagonals are congruent
trapezoid midsegment thm
the midsegment of a trapezoid is parallel to each base, and its length is 1/2 the sum of the lengths of he bases
