1. Quadrilaterals

2. Objectives
Properly use the terms, symbols, concepts, and the theorems in this chapter.
Determine and prove, if necessary, that a quadrilateral is a: parallelogram, rectangle, rhombus, square or trapezoid.

3. Properties of Parallelograms
Section 5-1
Properties of Parallelograms

4. Definitions
Quadrilateral:
Parallelogram:

5. Theorem 5-1

6. Theorem 5-2

7. Theorem 5-3

8. Practice and Assignment
Practice: Page 168
Assignment: Pages :1–31 odd, excluding 21, 27
Need to graph 17

9. Ways to Prove that Quadrilaterals are Parallelograms
Section 5-2
Ways to Prove that Quadrilaterals are Parallelograms

10. 5 ways to prove a Quadrilateral is a Parallelogram
Show that both pairs of opposite sides are parallel (definition).
Show that both pairs of opposite sides are congruent (theorem 5-4).
Show that one pair of opposite sides is both congruent and parallel (theorem 5-5).
Show that both pairs of opposite angles are congruent (theorem 5-6).
Show that the diagonals bisect each other (theorem 5-7).

11. Theorem 5-4

12. Theorem 5-5

13. Theorem 5-6

14. Theorem 5-7

15. Theorem 5-4 Proof

16. Practice and Assignment
Practice Page 173
Assignment: Pages : 2-24 evens, excluding 6, 18,

17. Theorems Involving Parallel Lines
Section 5-3
Theorems Involving Parallel Lines

18. Reminder
How do you find the distance from a point to a line?

19. Theorem 5-8

20. Theorem 5-9

21. Theorem 5-10

22. Theorem 5-11

23. Proving Theorem 5-11

24. Proving Theorem 5-11
The segment that joins the midpoints of two sides of a triangle is half as long as the third side.

25. Proving Theorem 5-11
What happens if you rotate the figure?

26. Practice and Assignment
Practice Page 179
Homework Pages :2-20 evens

27. Special Parallelograms
Section 5-4
Special Parallelograms

28. Objectives
Apply the definitions, identify special properties and apply theorems associated with the rectangle, rhombus, and square.

29. Definitions
Rectangle:
Rhombus:
Square:

30. Name that Quadrilateral

31. Questions about Quads. Is every square a rectangle?
Is every rectangle a square?
Is every rhombus a square?
Is every square a rhombus?
Is every rectangle a rhombus?
Is every rhombus a rectangle?
Is every rhombus/square/rectangle a parallelogram?
Is every parallelogram a square, rectangle or rhombus?

32. Theorem 5-12

33. Theorem 5-13

34. Theorem 5-14

35. Theorem 5-15

36. Theorems 5-16 and 5-17
5-16:
5-17:

37. Practice

38. Practice and Assignment
Practice: Page 186
Assignment: Pages :2-32 evens, excluding 22
Need Graph Paper

39. Section 5-5
Trapezoids

40. Objectives
A.Apply the definitions and theorems of trapezoid and isosceles trapezoid.
B.Identify the legs, bases, median and base angles of a trapezoid.

41. Definitions Trapezoid: Isosceles trapezoid: Median of a trapezoid:
Base angles of a trapezoid:

42. Parts of a Trapezoid

43. Theorem 5-18

44. Theorem 5-19

45. Practice and Assignment
Practice Page 192
Assignment: Pages ; 2-32 evens, excluding 12, 20, 24, 28

46. Assignment: Page 199 #2-18 evens
Chapter 5 Review
Quadrilaterals
Assignment: Page 199 #2-18 evens