Chapter 6.3

1. If opposite sides of a quadrilateral are //, then it is a //ogram. (definition) 2. If both pairs of opposite sides of a quadrilateral are , then it is a //ogram. 3. If both pairs of opposite angles are , then it is a //ogram.

4. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a //ogram. 5. If the diagonals bisect each other, then it is a parallelogram. 6. If one pair of opposite sides of a quadrilateral are // and , then it is a parallelogram. (new) (new) Additional Test for a //ogram

Yes.Opposite Angles are Congruent.

No, not enough information.

Yes.Opposite Sides are Parallel (definition).

Yes.One pair of opposite sides are parallel and congruent.

Yes.An angle is supplementary to both of its consecutive angles. 60 o 120 o

No, not enough information.

Yes.Opposite Sides are Congruent.

60 o 120 o No, not enough information.

Yes.Diagonals bisect each other.

No, not enough information.

Yes, Opposite sides are congruent. Others can be proven as well. A DC B  ABC   CDA

Distance Formula Distance Formula Midpoint Formula Slope  // lines have equal slope

Slope Method Prove AB//CD and BC//AD Prove AB//CD and BC//AD Use slope formula and show that their slopes are equal. Use slope formula and show that their slopes are equal. Distance Method Prove AB = CD and BC = AD Prove AB = CD and BC = AD Use Distance Formula to show that their lengths are equal. Use Distance Formula to show that their lengths are equal. Slope & Distance Prove AB = CD and AB // CD Use Distance Formula to show that their lengths are equal and use slope formula to show that their slopes are equal. Midpoint Method Prove the diagonals bisect each other Show that the diagonals have the same midpoint.

A.Both pairs of opp. sides . B.Both pairs of opp.  ’s . C.One pair of opp. sides both  and ||. D.Diagonals bisect each other Proof:Since ΔXVY  ΔZVW and ΔXVW  ΔZVY, by CPCTC. By which method would you prove WXYZ is a parallelogram?

Properties of Parallelograms Determine whether the quadrilateral is a parallelogram. Justify your answer. Answer:Each pair of opposite sides has the same measure. Therefore, they are congruent. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.

A.Both pairs of opp. sides ||. B.Both pairs of opp. sides . C.Both pairs of opp.  ’s . D.One pair of opp. sides both || and . Which method would prove the quadrilateral is a parallelogram?

Find x so that the quadrilateral is a //ogram. Opposite sides of a //ogram are congruent.

A.m = 2 B.m = 3 C.m = 6 D.m = 8 Find m so that the quadrilateral is a //ogram.

COORDINATE GEOMETRY Determine whether the figure with vertices A(–3, 0), B(–1, 3), C(3, 2), and D(1, –1) is a parallelogram. Use the Slope Formula. Use Slope and Distance

= slopes  // LinesOpp. Sides are //  //ogram

1. A 2. B 3. C Determine whether the figure with the given vertices is a parallelogram. Use the method indicated. A(–1, –2), B(–3, 1), C(1, 2), D(3, –1); Slope Formula A.yes B.no C.cannot be determined

Chapter 6.3  Pg 337: 3-14, 20-25, 26, 28, , 20-25, 26, 28, 45-48