1. Warm Up 01.12.12 Week 2 Find the value of a and b.

2. 1) AD =8 Re 1 2) EC =5 3) m ∠ ADC = 65 + 45 = 110º 3) m ∠ BCD = 180º - 110º = 70º

3. 45º Re 2 2) If alternate interior angles are congruent then the lines are parallel. ( T3.8) 1) Linear Pairs add up to 180º 135 + 45 = 180 45 = 45

4. Section 6.3 Day 1 I will prove that a quadrilateral is a parallelogram. Parallelograms - Opposite Sides Converse If both pairs of opposite sides of a quadrilateral are congruent, it is a parallelogram. Theorem 6.6 A BC D ABCD is a

5. Parallelograms - Opposite Angles Converse If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram. Theorem 6.7 A BC D ABCD is a

6. Parallelograms – Consecutive Angles Converse If an angle of a quadrilateral is supplementary to both of its consecutive sides, it is a parallelogram. Theorem 6.8 A BC D ABCD is a xº ( 180 – x )º

7. Parallelograms – Diagonals Converse If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Theorem 6.9 A BC D ABCD is a

8. Ex 1 Show that opposite sides are parallel. Prove ABCD is a ( 1, 3 ) +( -2, 1 ) ( -1, 4 ) = -4 4 = ( 6, 5 ) +( -7, -1 ) ( -1, 4 ) = -4 4 = Repeat for the other opposite sides. -4

9. Ex 1 Show that opposite sides are parallel. Prove ABCD is a ( 1, 3 ) +( -6, -5 ) ( -5, -2 ) ( 2, -1 ) +( -7, -1 ) ( -5, -2 ) 2 5 = 2 5 = -4 2 5 2 5

10. Handout - 6.3B except # 15 - will be done tomorrow. Assignment: Review Do 1:What value of x makes the shape a parallelogram? If an angle of a quadrilateral is _____ to both of its consecutive sides it is a parallelogram.