Special  Quadrilaterals Sect 5.10, 5.11, 5.12
Quadrilateral Four sided polygon
Foldable 1.  4 congruent sides and 4 congruent (right) angles 2.  All properties of parallelogram, rectangle, and rhombus ...
Foldable 1. Opposite sides parallel. 2.  Opposite sides congruent. 3.  Opposite angles are congruent. 4.  Consecutive angl...
Trapezoid ONE PAIR OF PARALLEL SIDES
A quadrilateral is a TRAPEZOID if and only if it has ONE pair of parallel sides
Trapezoid Leg angles are supplementary Leg angle 1 Leg angle 2 leg  leg base base
Trapezoid Theorem 8.17-Midsegment of a trapezoid is parallel to each base and is ½ the sum of the lengths of the bases Mid...
Trapezoid Theorem 8.14- If a  Trapezoid  is  Isosceles then Base angles are congruent Base angle 2 Base angle 1 leg  leg b...
Trapezoid Theorem 8.16- A trapezoid is isosceles if and only if its Diagonals are congruent
KITE TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES  (opposite sides not congruent)
A quadrilateral is a KITE if and only if it has two pairs of congruent consecutive sides
KITE Theorem 8.18-Diagonals are perpendicular
KITE Short diagonal is bisected
KITE Theorem 8.19-ONE pair of opposite angles are congruent  (not both)
KITE The other angles are bisected by the diagonal
Foldable QUADRILATERALS 1.  One pair of parallel sides 2.  Leg angles supplementary 3.  Midsegment= ½(b 1  + b 2 ) 4.  Iso...
Isosceles Trapezoid: 1.  2 pairs of congruent base angles 2.  Diagonals are congruent
Let's make a Venn Diagram Relating all of the Properities of our quadrilaterals
QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares
QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares 1. Diagonals bisect angles 2. Diag. perpendicular 3. 4 equal si...
QUADRILATERALS PARALLELOGRAMS RHOMBUSES RECTANGLES Squares 1. Diagonals bisect angles 2. Diag. perpendicular 3. 4 equal si...
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8 5 Trapezoid And Kites

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8 5 Trapezoid And Kites

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

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