Special Quadrilaterals   All Of Chapter 8
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Special Quadrilaterals All Of Chapter 8

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Special Quadrilaterals All Of Chapter 8 Presentation Transcript

  • 1. Special Quadrilaterals Sect 5.10, 5.11, 5.12
  • 2. Quadrilateral Four sided polygon
  • 3. Foldable 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line.
  • 4. Foldable 2. Now, divide the right hand section into 5 sections by drawing 4 evenly spaced lines. The fold crease 3. Use scissors to cut along your drawn line, but ONLY to the crease!
  • 5. Foldable 4. Write QUADRILATERALS down the left hand side The fold crease QUADRILATERALS
  • 6. Foldable 5. Fold over the top cut section and write PARALLELOGRAM on the outside. The fold crease Parallelogram 6. Reopen the fold. QUADRILATERALS
  • 7. Foldable 7. On the left hand section, draw a parallelogram. 8. On the right hand side, list all of the properties of a parallelogram. QUADRILATERALS
  • 8. Parallelograms Now, Let’s review what we learned last class
  • 9. A quadrilateral is a PARALLELOGRAM if and only if it has two sets of parallel sides
  • 10. Properties 1.BOTH pairs of opposite sides are parallel 2.BOTH pairs of opposite sides are congruent 3. BOTH pairs of opposite angles are congruent 4.Consecutive angles are supplementary 5.diagonals BISECT each other
  • 11. Foldable * Fold over the second cut section and write RECTANGLE on the outside. RECTANGLE * Reopen the fold. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. QUADRILATERALS
  • 12. Foldable * On the left hand section, draw a rectangle. * On the right hand side, list all of the properties of a rectangle. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. QUADRILATERALS
  • 13. RECTANGLE A parallelogram with FOUR RIGHT ANGLES
  • 14. A quadrilateral is a RECTANGLE if and only if it has four right angles
  • 15. RECTANGLE Diagonals are Congruent
  • 16. Foldable * Fold over the third cut section and write RHOMBUS on the outside. RHOMBUS * Reopen the fold. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. QUADRILATERALS
  • 17. Foldable * On the left hand section, draw a rhombus. * On the right hand side, list all of the properties of a rhombus. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. QUADRILATERALS
  • 18. RHOMBUS A parallelogram with FOUR CONGRUENT SIDES
  • 19. A quadrilateral is a RHOMBUS if and only if it has four congruent sides
  • 20. RHOMBUS Diagonals Bisect A Pair of Opposite Angles
  • 21. Diagonals are Perpendicular RHOMBUS
  • 22. Foldable * Fold over the fourth cut section and write SQUARE on the outside. SQUARE * Reopen the fold. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. QUADRILATERALS
  • 23. Foldable * On the left hand section, draw a square. * On the right hand side, list all of the properties of a square. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. QUADRILATERALS
  • 24. SQUARE A parallelogram with FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES
  • 25. A quadrilateral is a SQUARE if and only if it has four congruent sides and four right angles
  • 26. SQUARE Holds same properties as Rhombus and Rectangle
  • 27. Foldable 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus TRAPEZOID KITE 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. QUADRILATERALS
  • 28. Foldable 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus QUADRILATERALS
  • 29. Trapezoid ONE PAIR OF PARALLEL SIDES
  • 30. A quadrilateral is a TRAPEZOID if and only if it has ONE pair of parallel sides
  • 31. Trapezoid Leg angles are supplementary Leg angle 1 Leg angle 2 leg leg base base
  • 32. Trapezoid Midsegment is ½ the sum of the lengths of the bases Midsegment =½ (b 1 + b 2 ) Base (b 2 ) Base (b 1 )
  • 33. Trapezoid Isosceles: Base angles are congruent Base angle 2 Base angle 1 leg leg base base
  • 34. Trapezoid Isosceles: Diagonals are congruent
  • 35. KITE TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES (opposite sides not congruent)
  • 36. A quadrilateral is a KITE if and only if it has two pairs of congruent consecutive sides
  • 37. KITE Diagonals are perpendicular
  • 38. KITE Short diagonal is bisected
  • 39. KITE ONE pair of opposite angles are congruent (not both)
  • 40. KITE The other angles are bisected by the diagonal
  • 41. Foldable QUADRILATERALS 1. One pair of parallel sides 2. Leg angles supplementary 3. Midsegment= ½(b 1 + b 2 ) 4. Isosceles—see back 1. 2 pairs of consecutive sides congruent 2. 1 pair of opposite angles congruent 3. Diagonals perpendicular 4. Small diagonal bisected 5. Non-congruent angles are bisected 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus
  • 42. Isosceles Trapezoid: 1. 2 pairs of congruent base angles 2. Diagonals are congruent
  • 43. Let's make a Venn Diagram Relating all of the Properities of our quadrilaterals
  • 44. QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares
  • 45. QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares 1. Diagonals bisect angles 2. Diag. perpendicular 3. 4 equal sides 1. Polygon 2. 4 sides 1. 4 rt. angles 2. Diagonals congruent 5. Consecutive angles supplementary 4. Diagonals Bisect 3. Opposite Sides parallel 2. Opposite Angles congruent 1. Opposite Sides congruent
  • 46. QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares 1. Diagonals bisect angles 2. Diag. perpendicular 3. 4 equal sides 1. Polygon 2. 4 sides 1. 4 rt. angles 2. Diagonals congruent 5. Consecutive angles supplementary 4. Diagonals Bisect 3. Opposite Sides parallel 2. Opposite Angles congruent 1. Opposite Sides congruent Trapezoids Kites