1. Chapter 9
Quadrilaterals

2. Lesson #1 Polygons and Classifying Quadrilaterals
Essential Question #1
Explain why a square is a rectangle, but a rectangle is not a square.

3. Polygons Polygon Not a Polygon Polygon ABCDEF
A closed plane figure with at least 3 sides
The sides intersect only at their endpoints
Polygon
Not a Polygon A B C F E D
Polygon ABCDEF

4. Diagonals
The diagonals of a polygon are the segments that connects one vertex of a polygon to another non adjacent vertex. A B C F E D

5. A polygon is concave if a diagonal passes outside of the polygon.
Convex vs. Concave
A polygon is convex if no diagonals contain points outside the polygon.
A polygon is concave if a diagonal passes outside of the polygon.

6. Names of Polygons Polygon # of Sides 3 4 5 6 7 Polygon # of Sides 8 910 12 n

7. Polygon Angle Sum Theorem
Sides
Triangles
Degrees 3 4 5 6 7
Sides
Triangles
Degrees 8 9 10 12 n
The sum of the measures of the interior angles of a polygon with n sides is 180(n – 2).

8. Find the sum of the measures of the interior angles of each polygon.
Example 1
Find the sum of the measures of the interior angles of each polygon.
15-gon gon

9. Example 2
Find x:

10. Each exterior angle is supplementary to its adjacent interior angle.
Exterior Angles
An angle drawn on the outside of a polygon that is formed by extending one side.
Exterior
Angle
Each exterior angle is supplementary to its adjacent interior angle.

11. Polygon Exterior Angle Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°

12. Regular Polygons
A polygon whose sides are the same length and angles are the same measure.

13. Example 3
Find the measure of an interior angle and an exterior angle of a regular dodecagon.

14. Homework
Practice Worksheet 6-1

15. Quadrilaterals A quadrilateral is a polygon with 4 sides.
Depending upon its characteristics, a quadrilateral may have a special name.

16. A quadrilateral with exactly one pair of parallel sides
QUADRILATERALS
No pairs of parallel sides
Two pairs of parallel sides
One pairs of parallel sides
TRAPEZOID
KITES
PARALLELOGRAM
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
A quadrilateral with exactly one pair of parallel sides
A quadrilateral with both pairs of opposite sides parallel
RECTANGLE
RHOMBUS
ISOSCELES TRAPEZOID
SQUARE
A parallelogram with four congruent sides and four congruent angles
A trapezoid whose nonparallel sides are congruent
A parallelogram with four congruent angles
A parallelogram with four congruent sides

17. QUADRILATERALS No pairs of parallel sides Two pairs of parallel sides
One pairs of parallel sides

18. Determine the most precise name for quadrilateral LMNP.
Example 4
Determine the most precise name for quadrilateral LMNP. L M N P

19. Example 5
Find the value of the variables of the quadrilateral at the left is a kite. I E K T
2y + 5
x + 6
3x - 5
2x + 4

20. Homework
Page 94 #16, 18, 25-27

21. Properties of Parallelograms
Lesson #2
Properties of Parallelograms
Essential Question #2
Explain how the diagonal properties of a rhombus differ from those of a parallelogram.

22. Properties of a Parallelogram
Opposite sides are parallel (definition)
Opposites sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
The diagonals bisect each other.

23. Find the value of the missing angles.
Example 1
Find the value of the missing angles.
22° 3 2 1
45°
113° 3 2 1 4
47°
72°

24. Example 2
In parallelogram RSTV, diagonals RT and SV intersect at Q. If RQ = 5x – 1 and QT = 3x + 15, find QT.

25. QUADRILATERALS No pairs of parallel sides Two pairs of parallel sides
One pairs of parallel sides

26. Properties of a Rectangles
HAS ALL OF THE PROPERTIES OF A
PARALLELOGRAM.
4 Congruent Angles (by definition)
Diagonals are congruent.

27. Example 3
Find x.

28. Properties of a Rhombus
HAS ALL OF THE PROPERTIES OF A
PARALLELOGRAM.
Has 4 congruent sides (by definition)
Each diagonal bisects two angles
The diagonals are perpendicular.

29. Example 4
Find x.

30. Properties of a Square ALL OF THE PROPERTIES OF A PARALLELOGRAM.
ALL OF THE PROPERTIES OF A RECTANGLE.
ALL OF THE PROPERTIES OF A RHOMBUS.

31. Example 5
Find x.

32. Find each value of each missing angle.
Example 6
Find each value of each missing angle.

33. Find each value of each missing measure.
Example 7
Find each value of each missing measure.

34. Homework
Practice Worksheet 6.2, 6.4, 6.5

35. Lesson #3 Trapezoids, Isosceles Trapezoids, and Kites
Essential Question #3
Can two consecutive angles of a kite be supplementary? Why or why not?

36. Trapezoids
BASE
LEG
LEG
BASE ANGLES
BASE

37. Properties of a Trapezoid
Exactly one pair of opposite sides are parallel
(by definition)
Exactly two pairs of consecutive angles are
supplementary

38. Properties of a Isosceles Trapezoid
ALL OF THE PROPERTIES OF A TRAPEZOID
The legs are congruent (by definition)
The base angles are congruent
Diagonals are congruent

39. Find the missing angles.
Example 1
Find the missing angles.

40. Properties of Kites
Two sets of adjacent sides congruent (by definition)
The angles formed by the sides of differing lengths are
congruent
The diagonals are perpendicular
The diagonal connecting the non-congruent angles bisects
the other diagonal.

41. Find the missing angles.
Example 2
Find the missing angles.

42. Example 3
Find the side measures.

43. Homework
Page 473 #1-5, 13-16