Coordinate Geometry: Tests for Parallelograms (G.9)

Obj: SWBAT determine if a quadrilateral is a parallelogram (6.3/6.4/6.5).

WU: Triangles- graded*hw/hw log/graph paper/Storybook:”Quadrilaterals”

Wkb p. 155-156

HW (day 48): Regular worksheet day 50/Quiz (6.3-6.5)/Graph Paper

Honors: Wkb p. 155 (1, 6, 7, 8)/Quiz 6.3-6.5)/Graph Paper

Pearsonsuccess.net (due Friday)

Challenge: Girls versus BoysClassify the figure, given the coordinates.

ABCD is a ______A(-3, 2)B(-2, 6)C(2, 7)D(1, 3)ABCD is a rhombus

EFGG is a _______E (1, -2)F(13, 4)G(6, 8)H(-2, 4)EFGH is trapezoid

Proving Parallelograms

Thm: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Thm: If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

E

S I

D

**How would you prove the sides congruent?

** How would you prove the opposite angles congruent?

Thm: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Thm: If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

E

S I

D

E

S I

D

**How would you prove the sides congruent?

**How would you prove the sides congruent?

Find the values of x and y the ensure each quadrilateral is a parallelogram

Summary – Tests for Parallelograms1. Both pairs of opposite sides are parallel (Definition)2. Both pairs of opposite sides are congruent 3. Both pairs of opposite angles are congruent 4. Diagonal bisect each other 5. A pair of opposite sides are both parallel and

congruent