Parallelograms Flashcards
(20 cards)
What is a parallelogram?
Quadrilateral with both pairs of opposite sides parallel
What are the five ways to prove a quadrilateral is a parallelogram?
Both pairs of opposite sides parallel
Both pairs of opposite angles congruent
One pair of opposite sides are both congruent and parallel
Both pairs of opposite angles are congruent
Diagonals bisect each other
What are the properties of a parallelogram?
Opposite sides of a parallelogram are congruent
Opposite angles of a parallelogram are congruent
Diagonals of a parallelogram bisect each other
What are the three special parallelograms?
Rectangle
Square
Rhombus
What are the properties of a rectangle?
Quadrilateral with 4 right angles
Both pairs of angles congruent
Every rectangle is a parallelogram
What are the rectangle theorems?
Diagonals of a rectangle are congruent
If any angle of a parallelogram is a right angle, then the parallelogram is a rectangle
What are the properties of a rhombus?
Quadrilateral with 4 congruent sides
Both pairs of opposite sides congruent
Every rhombus is a parallelogram
What are the rhombus theorems?
Diagonals of a rhombus are perpendicular
Each diagonal of a rhombus bisects two angles of a rhombus
If two consecutive sides of a parallelogram are congruent then the parallelogram is a rhombus
What are the properties of a square?
Quadrilateral with 4 right angles and 4 congruent sides
Every square is a rectangle, rhombus and parallelogram
What do all of these special parallelograms have?
Properties of a parallelogram
If two lines are parallel…
Then all points on one line are equidistant from the other line
If 3 parallel lines cut off congruent segments on one transversal…
Then they cut off congruent segments on very transversal
A line that contains the midpoint of one side of a triangle and is parallel to another side…
Passes through the midpoint of the third side
The segment that joins the midpoints of two sides of a triangle is…
Parallel to the third side and half as long as the third side
What is a trapezoid?
Quadrilateral with exactly one pair of parallel sides
What is a base?
What is a leg?
Base: parallel side
Leg: other pair of sides
What is a trapezoid with congruent legs called?
Isosceles trapezoid
Base angles of an isosceles trapezoid are…
Congruent
What is the median of a trapezoid?
Segment which joins the midpoints of the legs
Only 1 median in trapezoid, many in triangles
The median of a trapezoid is…
Parallel to the bases and is the average of the base lengths
