Quadrilaterals Flashcards
rectangle
parallelogram
all angles right angles
diagonals congruent
Parallelogram
opposite sides parallel opposite sides congruent opposite angles congruent diagonals bisect each other any pair of consecutive angles are supplementary
kite
two disjoint pairs of consecutive sides congruent
diagonals perpendicular
one diagonal is perpendicular bisector of the other
one of diagonals bisects pair of opposite angles
one pair of opposite angles congruent
rhombus
parallelogram
kite
all sides congruent
diagonals bisect angles
diagonals perpendicular bisectors of each other
diagonals divide rhombus into four congruent right triangles
square
rhombus
rectangle
diagonals form four isosceles right triangles
isosceles trapezoid
legs congruent bases parallel lower base angles congruent upper base angles congruent diagonals congruent any lower base angle is supplementary to any upper base angle
polygon
plane figures
convex polygon
interior angles measure less than 180 degrees
How do you prove a quadrilateral is a parallelogram?
both pairs of opposite sides parallel both pairs of opposite sides congruent one pair of opposite sides parallel and congruent diagonals bisect each other both pairs of opposite angles congruent
How do you prove a quadrilateral is a rectangle?
parallelogram then one right angles
parallelogram then diagonals congruent
all four angles right angles
How do you prove a quadrilateral is a kite?
two disjoint pairs of consecutive sides of a quadrilateral are congruent
one of diagonals of quadrilateral is perpendicular bisector of another diagonal
How do you prove a quadrilateral is a rhombus?
parallelogram with pair of consecutive sides congruent
diagonal of parallelogram bisects two angles
diagonals perpendicular bisectors of each other
How can you prove a quadrilateral is a square?
rectangle and rhombus
How do you prove that a trapezoid is isosceles?
If the legs are congruent
If the lower or upper base angles are congruent
If the diagonals are congruent
