Download Five Ways to Prove that a Quadrilateral is a parallelogram

Notes #23: Proving Quadrilaterals are Parallelograms and other Theorems involving
Parallel Lines
Five Ways to Prove that a Quadrilateral is a parallelogram
1. Show that both pairs of opposite sides are parallel
2. Show that both pairs of opposite sides are congruent
3. Show that one pair of opposite sides are both congruent and parallel
4. Show that both pairs of opposite angles are congruent
5. Show that the diagonals bisect eachother.
So… if the picture shows any of these 5 qualities, then it is a parallelogram.
Theorems Involving Parallel Lines
5-9 If three parallel lines cut off congruent segments on one transversal, then they cut off
congruent segments on every transversal
5-10 If a line that contains the midpoint of one side of triangle and is parallel to another side,
then the line passes thru the midpoint of the third side.
5-11 The segment that joins the midpoints of two sides of a triangle is parallel to the third side
and is half as long as the third side.