Mr. Rodriquez used the parallelogram below to design a herringbone pattern for a paving stone. He will use the paving stone for a sidewalk. If m∠1.

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Mr. Rodriquez used the parallelogram below to design a herringbone pattern for a paving stone. He will use the paving stone for a sidewalk. If m∠1 is 130, find m∠2, m∠3, and m∠4. Problem of the Day

Section 6-3 Tests for Parallelograms

Then Now Objectives You recognized and applied properties of parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram in the coordinate plane.

Common Core State Standards Content Standards G.CO.11 – Prove theorems about parallelograms. G.GPE.4 – Use coordinates to prove simple geometric theorems algebraically. Mathematical Practices 2) Reason abstractly and quantitatively. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Conditions for Parallelograms If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. Conditions for Parallelograms

Determine whether the quadrilateral is a parallelogram Determine whether the quadrilateral is a parallelogram. Justify your answer. Example 1

Determine whether the quadrilateral is a parallelogram Determine whether the quadrilateral is a parallelogram. Justify your answer. Example 1

Determine whether the quadrilateral is a parallelogram Determine whether the quadrilateral is a parallelogram. Justify your answer. Example 1

Find x and y so that each quadrilateral is a parallelogram. Example 3

Find x and y so that each quadrilateral is a parallelogram. Example 3

Find x and y so that each quadrilateral is a parallelogram. Example 3

Determine whether quad ABCD is a parallelogram Determine whether quad ABCD is a parallelogram. Justify your answer using the distance formula. A(3, 3) B(8, 2) C(6, -1) D(1, 0) Example 4

Determine whether quad FGHI is a parallelogram Determine whether quad FGHI is a parallelogram. Justify your answer using the midpoint formula. F(-2, 4) G(4, 2) H(4, -2) I(-2, -1) Example 4

Determine whether quad QRST is a parallelogram Determine whether quad QRST is a parallelogram. Justify your answer using the slope formula. Q(-1, 3) R(3, 1) S(2, -3) T(-2, -1) Example 4

p.417 #4 – 7, 9 – 14, 18, 19 Homework