TechMathI - 5.3 - Properties of Quadrilaterals
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TechMathI - 5.3 - Properties of Quadrilaterals

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TechMathI - 5.3 - Properties of Quadrilaterals TechMathI - 5.3 - Properties of Quadrilaterals Presentation Transcript

  • Special Quadrilaterals
  • Quadrilateral Four sided polygon
  • 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. View slide
  • 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! View slide
  • Foldable 4. Write QUADRILATERALS down the left hand side The fold crease QUADRILATERALS
  • Foldable 5. Fold over the top cut section and write PARALLELOGRAM on the outside. The fold crease Parallelogram 6. Reopen the fold. QUADRILATERALS
  • 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
  • Parallelograms
  • A quadrilateral is a PARALLELOGRAM if and only if it has two sets of parallel sides
  • 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
  • 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. QUADRILATERALS
  • 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
  • RECTANGLE 1. A parallelogram with FOUR RIGHT ANGLES
  • Properties 2. Diagonals are congruent 3. Opposite sides congruent.
  • 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. Opposite sides congruent. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. QUADRILATERALS
  • 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
  • RHOMBUS 1. A parallelogram with FOUR CONGRUENT SIDES
  • RHOMBUS 2. Diagonals Bisect Opposite Angles
  • 3. Diagonals are Perpendicular RHOMBUS
  • 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
  • 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
  • SQUARE 1. A parallelogram with FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES
  • SQUARE Holds same properties as Rhombus and Rectangle
  • Foldable 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus TRAPEZOID 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
  • 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
  • Trapezoid 1. ONE PAIR OF PARALLEL SIDES
  • Trapezoid 2. Leg angles are supplementary Leg angle 1 Leg angle 2 leg leg base base
  • Trapezoid 3. Isosceles: Base angles are congruent Base angle 2 Base angle 1 leg leg base base
  • 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
  • Name the sides adjacent to MN. Name the angle opposite <N. If MN || OP and NO || MP then MNOP is a _____ . If NO || MP are the only pair of parallel segments then MNOP is a __________ . M N O P
  • x 2x Solve for x.
  • 78 92 x 42 Solve for x.