1. Chapter 6
Quadrilaterals

2. 6.1 Classifying Quadrilaterals
Parallelograms
Both pairs of opposite sides are parallel
Rhombus
Four congruent sides
Rectangle
Four right angles
Square
Four congruent sides and four congruent angles
Kite
Two pairs of adjacent sides congruent and no opposite sides congruent
Trapezoid
Exactly one pair of parallel sides
Isosceles Trapezoid
Nonparallel sides are congruent

3. Classifying Quadrilaterals
1. Is a square always a rectangle?

4. Classifying Quadrilaterals
2. Is a rectangle always a square?

5. Classifying Quadrilaterals
3. Is a square always a rhombus?

6. Classifying Quadrilaterals
4. Is a rhombus always a square?

7. Classifying Quadrilaterals
5. Is a square always parallelogram?

8. Classifying Quadrilaterals
6. Is a kite always parallelogram?

9. Classifying Quadrilaterals
7. Are there any shapes that are always parallelograms?

10. Classifying Quadrilaterals
Make a concept map
Include all quadrilaterals
Provide pictures, definitions, or key information needed to link the quadrilaterals

12. Quadrilaterals Parallelogram Kite Trapezoid Rhombus Rectangle
Isosceles Trapezoid
Square

13. Using properties of special quadrilaterals
Find the values of the variables for the kite. Then find the length of each side.

14. You try
Find the values of the variables.
x= _________,y=_____________

15. Assignment
Worksheet and Pg

16. 6.2 Properties of Parallelograms
What do you think the properties of a parallelogram are? Sides? Angles?

17. Prove opposite sides of a parallelogram are congruent
Given: ABCD is a Parallelogram
Prove: B C A D

18. Properties of Parallelograms
6-1 Opposite sides of a parallelogram are congruent.
6-2 Opposite angles of a parallelogram are congruent
Consecutive angles of a parallelogram are supplementary

19. Diagonals of a Parallelogram
Properties of parallelogram 6.2.gsp
Theorem 6-3
The diagonal of a parallelogram bisect each other.

20. Theorem 6- 4
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

21. Assignment
H:\Geometry\lessons\Chapter 6.ppt
Pg 315, 1-41 odd

22. 6.3 Proving that a Quadrilateral is a Parallelogram
text book site
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.

23. More Theorems
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
If one pair of opposites sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

24. Assignment
Pg 324, 1-10

25. 6.4 Special Parallelograms
Properties of Rhombuses 6.4.gsp
6-9 Each diagonal of a rhombus bisects two angles of the rhombus.
6-10 The diagonals of a rhombus are perpendicular.
Diagonals of a Rectangle 6.4.gsp
6-11 The diagonals of a rectangle are congruent.

26. Is the parallelogram a rhombus or a rectangle?
6-12 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.
6-13 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
6-14 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

27. Assignment
Pg 332, 1-17 odd all

28. 6.5 Trapezoids and Kites Trapezoids
6-15 The base angles of an isosceles trapezoid are congruent.
6-16 The diagonals of an isosceles trapezoid are congruent.

29. Kites
6.5 Kite.gsp
6-17 The diagonals of a kite are perpendicular.

30. Assignment
Pg 338, 1-6 all, 8-16 even