1. The Quadrilateral Family Tree Parallelograms I can use the properties of a parallelogram to solve problems.

2. 1. _____________________ ____________ _________ 1. _____________________ ________________________ 1. _____________________ 2. _____________________ 3. _____________________ 4. _____________________ _____________________ 2. _____________________ 1. _____________________ _____________________ 2. _____________________ 3. _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________ 3. _______________ __________ 1. _____________________ 2. _____________________ 3. _____________________ __________________

3. 1. _____________________ _____________________ Quadrilateral 1. _____________________ 2. _____________________ 3. _____________________ 4. _____________________ _____________________ 2. _____________________ 1. _____________________ _____________________ 2. _____________________ 3. _____________________ 1. _____________________ _____________________ 1. _____________________ 2. _____________________ 3. _____________________ 4. _____________________ _____________________ 1. _____________________ 2. _____________________ 3. _______________ __________ 1. _____________________ 2. _____________________ 3. _____________________ __________________ 1. Four-sided polygon

5. Parallelogram A quadrilateral with two pairs of parallel sides

6. 1. T RAPEZOID 1. Four-sided polygon QUADRILATERAL 1. 2. 3. 4. P ARALLELOGRAM 2. 1. S QUARE 2. 3. 1. 2. 3. 4. 1. 2. 3. K ITE 1. 2. 3. I SOSCELES T RAPEZOID

7. Parallelogram – How can we construct a parallelogram?

8. Parallelogram

9. 1 2

10. 1 2

11. 1 2 3 4

12. 1 2 3 4

13. 1 2 3 4

14. 1 2 3 4

15. 1 2 3 4 The two triangles formed by a diagonal are congruent by ASA.

16. Parallelogram 1 2 3 4 What does that mean about opposite sides of a parallelogram?

17. Parallelogram 1 2 3 4 What does that mean about opposite sides of a parallelogram? CPCTC

18. 1. TRAPEZOID 1. Four-sided polygon Q UADRILATERAL 1. 2. 3. 4. PARALLELOGRAM 2. 1. S QUARE 2. 3. 1. R ECTANGLE 1. 2. 3. 4. R HOMBUS 1. 2. 3. K ITE 1. 2. 3. I SOSCELES T RAPEZOID

19. 1. 1. Four-sided polygon QUADRILATERAL 2. 3. 4. P ARALLELOGRAM 2. 1. S QUARE 2. 3. 1. 2. 3. 4. 1. 2. 3. 1. Opposite sides are congruent 2. 3. 1.

20. Parallelograms What about opposite angles in a parallelogram?

21. 1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent 3. 4. P ARALLELOGRAM 2. 1. S QUARE 2. 3. 1. 2. 3. 4. 1. 2. 3. 1. Opposite sides are congruent 2. 3. 1.

22. Parallelograms 1 2 Are these two triangles congruent? By which postulate?

23. Parallelogram Since the triangles are congruent, the diagonals of the parallelogram bisect each other.

24. 1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent 3. Diagonals bisect each other 4. P ARALLELOGRAM 2. 1. S QUARE 2. 3. 1. 2. 3. 4. 1. 2. 3. 1. Opposite sides are congruent 2. 3. 1.

25. Parallelogram 5 6 What kind of angles are angles 5 & 6?

26. Consecutive angles in a parallelogram are supplementary. Parallelogram 5 6

27. 1. 1. Four-sided polygon QUADRILATERAL 2. Opposite angles are congruent 3. Diagonals bisect each other 4. Consecutive angles are supp. P ARALLELOGRAM 2. 1. S QUARE 2. 3. 1. 2. 3. 4. 1. 2. 3. 1. Opposite sides are congruent 2. 3. 1.

28. Example In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF. Find mEFC. Find DF. CF = 74 mm  opp. sides  mEFC + mFCD = 180° mEFC = 138°  cons. s supp. DF = 2DG DF = 62  diags. bisect each other.

29. In KLMN, LM = 28 in., LN = 26 in., and mLKN = 74°. Find KN. Find mNML. Find LO. LM = 28 in.  opp. sides  Your Turn NML  LKN mNML = 74°  opp. s  LN = 2LO LO = 13 in.  diags. bisect each other.

30. WXYZ is a parallelogram. Find YZ. YZ = 52 Example

31. WXYZ is a parallelogram. Find mZ. Example mZ = 65°

32. EFGH is a parallelogram. Find JG. JG = 12 Example

33. EFGH is a parallelogram. Find FH. FH = 18 Your Turn

34. QRST is a parallelogram. Find each measure. 3. TQ *4. mT Lesson Quiz In PNWL, NW = 12, PM = 9, and mWLP = 144°. 1. PW 2. mPNW 18 144° 28 71°