This document discusses different types of quadrilaterals including trapezoids, kites, parallelograms, rectangles, rhombuses, and squares. It provides definitions and properties for each shape. Key properties include: 1) A trapezoid has one pair of parallel sides, leg angles are supplementary, and the midsegment is half the sum of the bases. 2) A kite has two pairs of consecutive congruent sides, diagonals are perpendicular, and one pair of opposite angles are congruent. 3) Parallelograms have opposite sides parallel and opposite angles congruent. Rectangles and squares are types of parallelograms with right angles or all sides congruent,

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