1. Lesson 7.6
Parallelograms pp

2. Objectives: 1. To prove the SAS Congruence Theorem for parallelograms.
2. To identify and prove the basic properties of parallelograms.

3. Theorem 7.15
The opposite sides of a parallelogram are congruent.

4. Theorem 7.15
The opposite sides of a parallelogram are congruent.

5. Theorem 7.16
SAS Congruence for Parallelograms. A B C D P Q R S

6. Theorem 7.17
A quadrilateral is a parallelogram if and only if the diagonals bisect one another.

7. Theorem 7.18
Diagonals of a rectangle are congruent.

8. Theorem 7.19
The sum of the measures of the four angles of every convex quadrilateral is 360°. B A C D

9. Theorem 7.20
Opposite angles of a parallelogram are congruent.

10. Theorem 7.21
Consecutive angles of a parallelogram are supplementary. 2 1

11. Theorem 7.22
If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

12. Theorem 7.23
A quadrilateral with one pair of parallel sides that are congruent is a parallelogram.

13. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No

14. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No A B D C
68°
112°

15. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No

16. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No

17. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No
100°
80°

18. Practice: Determine whether the given figure must be a parallelogram
Practice: Determine whether the given figure must be a parallelogram. Be ready to explain your answer.
1. Yes 2. No
120°
60°

19. Homework pp

20. ►A. Exercises
Using parallelogram ABCD, find the measures of the indicated angles.
1. C A D B C
48º
55º

21. ►A. Exercises
Using parallelogram ABCD, find the measures of the indicated angles.
2. ADC A D B C
48º
55º

22. ►A. Exercises
Using parallelogram ABCD, find the measures of the indicated angles.
3. ABD A D B C
48º
55º

23. ►A. Exercises
Using parallelogram ABCD, find the measures of the indicated angles.
4. The four angles of the parallelogram combined A D B C
48º
55º

24. ►A. Exercises
Using parallelogram ABCD, find the measures of the indicated angles.
5. An exterior angle of the parallelogram at angle C A D B C
48º
55º

25. ►A. Exercises 6. Adjacent angles form a linear pair.
Disprove the following statements. Remember that you disprove a statement by proving that it is false. This can be done with an illustration or a counterexample.
6. Adjacent angles form a linear pair.

26. ►A. Exercises 7. Alternate interior angles are congruent.
Disprove the following statements. Remember that you disprove a statement by proving that it is false. This can be done with an illustration or a counterexample.
7. Alternate interior angles are congruent.

27. ►A. Exercises
Disprove the following statements. Remember that you disprove a statement by proving that it is false. This can be done with an illustration or a counterexample.
8. Every pair of supplementary angles form a linear pair.

28. ►A. Exercises 9. The acute angles of a triangle are complementary.
Disprove the following statements. Remember that you disprove a statement by proving that it is false. This can be done with an illustration or a counterexample.
9. The acute angles of a triangle are complementary.

29. ►A. Exercises
Disprove the following statements. Remember that you disprove a statement by proving that it is false. This can be done with an illustration or a counterexample.
10. If two triangles have a pair of congruent angles, then the other pairs of angles are congruent.

30. ►B. Exercises
12. Given: ABCD with diagonals AC and BD bisecting each other at E
Prove: ABCD is a parallelogram A D B C E

31. ►B. Exercises
12. Given: ABCD with diagonals AC and BD bisecting each other at E
Prove: ABCD is a parallelogram A D B C E

32. ►B. Exercises 14. Given: Convex quadrilateral ABCD
Prove: mABC + mBCD + mCDA + mDAB = 360º C D B A

33. ►B. Exercises 16. Given: ABCD is a parallelogram
Prove: A & B are supplementary C B 3 1 2 D A

34. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
25. distances

35. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
26. bisectors

36. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
27. one triangle

37. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
28. two triangles

38. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
29. a circle

39. ■ Cumulative Review
Suppose two segments must be proved congruent. What reason could you use that involves the concept named?
30. a parallelogram

40. Analytic Geometry
Midpoints

41. If M is the midpoint of AB where A(x1, y1) and B(x2, y2),
Midpoint Formula
If M is the midpoint of AB where A(x1, y1) and B(x2, y2), ÷ ø ö ç è æ + = 2 y x
then 1 , M

42. Find the coordinate of the midpoint between the points (3, -5) and (1, -6).÷ ø ö ç è æ - + = 2 6 5 1 3 M ) ( , ÷ ø ö ç è æ - = 2 11 ,

43. Find the coordinate of the midpoint between the two points.
1. (4, 8) and (2, -3)

44. Find the coordinate of the midpoint between the two points.
2. (3, 5) and (3, 9)

45. Find the coordinate of the midpoint between the two points.
3. (-1, -4) and (6, -2)