1. SECTION 8-2, 8-4, 8-5 spi.3.2.H Jim Smith JCHS

2. Parallelograms are quadrilaterals with Both pairs of opposite sides parallel. ABCD A B CD › › › › › ›

3. 5 Things About Parallelograms Definition 1) Both Pairs Opp Sides Parallel Properties 2) Both Pairs Opp Sides Congruent 3) Both Pairs Opp Angles Congruent 4) Consecutive Angles Supplementary 5) Diagonals Bisect Each Other

4. Both Pairs Opp Sides Parallel Alternate Int Angles Are Congruent 1 2 3 4 5 6 7 8 DC B A AB||DC 1 and 6 3 and 8 AD||BC 2 and 5 4 and 7

5. Both Pairs Opp Sides Congruent 23 X 42 2Y - 16 X = 23 X = 23 2Y – 16 = 42 2Y = 58 2Y = 58 Y = 29 Y = 29

6. Both Pairs Opposite Angles Congruent 65° 5Y - 5 115° X X = 65 X = 65 5Y – 5 = 115 5Y = 120 5Y = 120 Y = 24 Y = 24

7. Consecutive Angles Are Supplementary 1 2 3 4 Supplementary angles have a sum of 180

8. Diagonals Bisect Each Other A B C D X || | | || BX = XD AX = XC

9. Rectangles Are Parallelograms With 4 Right Angles All 5 Things About Parallelograms Are True… PLUS 1) All angles = 90° 2) Diagonals are congruent

10. All Angles = 90° If 1 Angle In A Parallelogram Is A Right Angle, Then All 4 Angles Are Right Angles This gives us right triangles also

11. Diagonals Are Congruent This Gives Us 4 Congruent Segments And 4 Isosceles Triangles This Tells Us A Lot About The Angles | | | |

12. 1 2 3 4 5 67 11 12 109 8 Congruent Pairs of Angles

13. 1 2 3 4 5 67 11 12 109 8

14. A Rhombus Is A Parallelogram With 4 Congruent Sides All 5 Things About Parallelograms Are True…PLUS 1) 4 congruent sides 2) Diagonal are perpendicular 3) Diagonals bisect opposite angles

15. 4 congruent sides 10 3Y + 1 3Y + 1 = 10 3Y = 9 3Y = 9 Y = 3 Y = 3

16. Diagonal are perpendicular AB CD X 34 AB = The perimeter Of rhombus ABCD = XC = DB = 5 20 3 8

17. The Square Is The Most Special Of All !! Everything That’s True For Everything That’s True For All The Others Is True For All The Others Is True For Squares.

18. PARALLELOGRAMS QUADRILATERALS RECTANGLESRHOMBI SQUARES