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8 5 Trapezoid And Kites
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8 5 Trapezoid And Kites

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  • 1. Special Quadrilaterals Sect 5.10, 5.11, 5.12
  • 2. Quadrilateral Four sided polygon
  • 3. 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
  • 4. 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
  • 5. Trapezoid ONE PAIR OF PARALLEL SIDES
  • 6. A quadrilateral is a TRAPEZOID if and only if it has ONE pair of parallel sides
  • 7. Trapezoid Leg angles are supplementary Leg angle 1 Leg angle 2 leg leg base base
  • 8. Trapezoid Theorem 8.17-Midsegment of a trapezoid is parallel to each base and is ½ the sum of the lengths of the bases Midsegment =½ (b 1 + b 2 ) Base (b 2 ) Base (b 1 )
  • 9. Trapezoid Theorem 8.14- If a Trapezoid is Isosceles then Base angles are congruent Base angle 2 Base angle 1 leg leg base base
  • 10. Trapezoid Theorem 8.16- A trapezoid is isosceles if and only if its Diagonals are congruent
  • 11. KITE TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES (opposite sides not congruent)
  • 12. A quadrilateral is a KITE if and only if it has two pairs of congruent consecutive sides
  • 13. KITE Theorem 8.18-Diagonals are perpendicular
  • 14. KITE Short diagonal is bisected
  • 15. KITE Theorem 8.19-ONE pair of opposite angles are congruent (not both)
  • 16. KITE The other angles are bisected by the diagonal
  • 17. 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
  • 18. Isosceles Trapezoid: 1. 2 pairs of congruent base angles 2. Diagonals are congruent
  • 19. Let's make a Venn Diagram Relating all of the Properities of our quadrilaterals
  • 20. QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares
  • 21. 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
  • 22. 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