1. Chapter 6 Section 6.1 – Classifying Quadrilaterals
Objectives: To define and classify special types of quadrilaterals

2. Definitions -> Special Quadrilaterals
Parallelogram -> a quadrilateral with both pairs of opposite sides parallel
Rhombus -> a parallelogram with four congruent sides
Rectangle -> a parallelogram with four right angles
Square -> a parallelogram with four congruent sides and four right angles
Kite -> a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
Trapezoid -> a quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid -> a trapezoid whose nonparallel opposite sides are congruent

3. Ex: Classifying a Quadrilateral
Classify the following figures in as many ways as possible

4. Ex: Using the Properties of Special Quadrilaterals
Find the values of the variable for the kite T
2y + 5
x + 6 J K
2x + 4
3x - 5 B

5. Ex:
Find the values of the variables for the rhombus. Then find the lengths of each side. L
3b + 2 N
5a + 4
3a + 8 S T
4b - 2

6. Homework #31
Due Tuesday (December 04)
Page 308 – 309
# 1 – 12 all
# 13 – 25 all

7. Section 6.2 Properties of Parallelograms
Objectives: To use relationships among sides and among angles of parallelograms
To use relationships involving diagonals of parallelograms or transversals

8. Theorem 6.1 Opposite sides of a parallelogram are congruent
Consecutive Angles -> angles of a polygon that share a side. Since a parallelogram has opposite sides parallel, consecutive angles are same-side interior angles (supplementary) D C
<A and <B
<B and <C
<C and <D
<D and <A A B

9. Ex: Using Consecutive Angles
Find the measure of each missing angle in parallelogram RSTW S T
112° R W

10. Theorem 6.2 Ex: Opposite angles of a parallelogram are congruent
Find the value of x and y in parallelogram PQRS. Then find the measures of each side and each angle. Q
3x - 15 R
(3y + 37)°
(6y + 4)° P S
2x + 3

11. Theorem 6.3 The diagonals of a parallelogram bisect each other
JH congruent LH KH congruent MH J K H M L

12. Ex:
Find the value of x and y. Then find the value of each line segment B C 2x
x + 1 E
3y - 7 y A D

13. 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. A B C D E F

14. Homework #32
Due Wednesday (Dec 05)
Page 315 – 316
# 1 – 13 all
# 14 – 30 even

15. Section 6.3 - Proving that a Quadrilateral is a Parallelogram
Objectives: To determine whether a quadrilateral is a parallelogram

16. Theorem 6.5
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
Since both pairs of opposite sides are congruent, the above quadrilateral is also a parallelogram.

17. Theorem 6.6
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Since both pairs of opposite angles are congruent, the above quadrilateral is also a parallelogram.

18. Theorem 6.7
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Since the diagonals are bisected, the above quadrilateral is also a parallelogram.

19. Theorem 6.8
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Since one pair of opposite sides are parallel and congruent, the above quadrilateral is also a parallelogram.

20. Ex: Finding Values for Parallelograms
For what values of x and c must MLPN be a parallelogram? P L y
2y - 7
3c - 3
c + 1 3x
y + 2 M N

21. Homework #33
Due Thursday (Dec 06)
Page 324 – 325
# 1 – 19 all

22. Section 6.4 Special Parallelograms
Objectives: To use properties of diagonals of rhombuses and rectangles
To determine whether a parallelogram is a rhombus or a rectangle

23. Theorem 6.9
Each diagonal of a rhombus bisects two angles of the rhombus B C 3 4
< 1 congruent < 2
< 3 congruent < 4 1 2 A D

24. Theorem 6.10 The diagonals of a rhombus are perpendicular C B
AC perpendicular BD A D

25. Theorem 6.11 The diagonals of a rectangle are congruent A D
AC congruent BD B C

26. Theorem 6.12 Theorem 6.13 Theorem 6.14
If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.
Theorem 6.13
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6.14
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

27. Homework # 34
Due Monday (December 10)
Page 332 – 334
# 1 – 17 odd
# 41 – 46 all

28. Section 6.5 Trapezoids and Kites
Objectives: To verify and use properties of trapezoids and kites

29. Base Angles -> two angles that share a base of a. trapezoid
Base Angles -> two angles that share a base of a trapezoid. Since the bases of the trapezoid are parallel, the two angles that share a leg are supplementary.
Base Angles
Leg
Leg
Base Angles

30. Theorem 6.15
The base angles of an isosceles trapezoid are congruent
Ex:
Find the measure of each angle in the following trapezoid B C P Q
102°
70° S R A D

31. Theorem 6.16
The diagonals of an isosceles trapezoid are congruent
Theorem 6.17
The diagonals of a kite are perpendicular

32. Ex: Find the measures of < 1, < 2, and < 3 in the kite B 3
32° 1 2 A C D

33. Chapter 6 Test Thursday/Friday
Homework # 35
Due Monday (December 10)
Page 338 – 340
# 1 – 27 odd
Quiz Tuesday (Dec 11)
Chapter 6 Test Thursday/Friday