7.2 Properties of Parallelograms

What is a Parallelogram? Definition: A quadrilateral where both pairs of opposite sides are parallel. Properties: Let’s Investigate.

Open up a new Geogebra file 1) Construct a parallelogram by constructing two pairs of parallel lines. 2) Come up with 4 conjectures about a) opposite angles b) opposite sides c) consecutive angles d) the diagonals

5 Facts about Parallelograms 1)Definition: Opposite Sides are Parallel. 2)Property: Opposite Sides are Congruent 3)Property: Opposite Angles are Congruent 4)Property: Consecutive Angles are Supplementary 5)Property: The diagonals bisect each other.

LETS PROVE THEM. WHAT TYPE OF REASONING ARE WE ABOUT TO USE?

Prove the Parallelogram Opposite Sides Theorem Given: ABCD is a parallelogram.

Prove the Parallelogram Opposite Angles Theorem Given: ABCD is a parallelogram.

Prove the Parallelogram Consecutive Angles Theorem Given: ABCD is a parallelogram.

Prove the Parallelogram Diagonals Theorem Given: ABCD is a parallelogram.

Parallelogram in the Coordinate Plane (Dat GP) Given the coordinates of the intersection of the diagonals of LMNO with vertices L(1,4) M(7,4) N(6,0) 0(0, 0), find where the diagonals will intersect. (use the Diagonals Theorem) Given three vertices, find the coordinates of Y such that makes WXYZ a parallelogram; W(-1, -3), X(-3, 2), Z(4, -4).

Challenge Proof

Exit Ticket List the 5 things you can assume given a parallelogram ABCD.