2.3b:Quadrilaterals - Tests for Parallelograms M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving polygons GSE’s CCSS:

Th. 6-5 : If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A B RT What does this tell us ?

Th. 6-6: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. A W P Q What does this tell us?

Th. 6-7: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. H P M B G

Th. 6-8: If one pair of opposite sides of a quadrilateral is both parallel and Congruent, then the quadrilateral is a parallelogram. OR

The coordinates of the vertices of quadrilateral EFGH are E (6,5) F (6,11) G (14,18) H ( 14,12) Determine if EFGH is a parallelogram. Justify your answer mathematically

Determine whether the quadrilateral SNOW with the given Vertices is a parallelogram by Diagonals bisecting each other S (7,4) N (5,1) O (0,0) W (2,3)

Find the possible coordinates For the 4 th vertex of a Parallelogram with vertices A, B, and C

Find the coordinates Of all possible Coordinates for the 4 th vertices of the parallelogram

, 1 1 Statement Reasons Given: Prove: Given