1. G-4 “I can prove theorems about parallelograms”
6-2, 6-3, 6-4

2. Each segment that forms a polygon is a side of the polygon
Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

3. You can name a polygon by the number of its sides
You can name a polygon by the number of its sides. The table shows the names of some common polygons.

4. Check it out 1
Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. 1a. 1b. 1c.

5. Don’t Write:
Any polygon with four sides is a quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names.
Opposite sides of a quadrilateral do not share a vertex. Opposite angles do not share a side.
Helpful Hint

6. Parallelogram
A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol .

11. Example 1 In CDEF, DE = 74 mm, DG = 31 mm, mFCD = 42°. Find CF.
Find mEFC.
Find DF

12. Example 2
WXYZ is a parallelogram. Find YZ ___and mZ ____

13. Example 3
EFGH is a parallelogram. Find JG ____ and FH ____

14. In KLMN, LM = 28 in., LN = 26 in., mLKN = 74° Find KN = ____, mNML = _____, LO = _____

17. To show that a quadrilateral is a parallelogram, you only have to show that it satisfies one of these sets of conditions.
Helpful Hint

18. Example 4
Show that JKLM is a parallelogram for a = 3 and b = 9.

19. Example 5
Show that PQRS is a parallelogram for x = 10 and y = 6.5.

20. Show that PQRS is a parallelogram for a = 2.4 and b = 9.

22. Special Parallelograms
A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.

25. Example 6
A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM ______ and ML ______

26. Example 7
The rectangular gate has diagonal braces. Find HJ _____

27. A rhombus is another special quadrilateral
A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.

29. Rhombus

30. Example 8
CDFG is a rhombus. Find CD _____

31. Example 9
CDFG is a rhombus. If mGCD = (b + 3)° and mCDF = (6b – 40)°. Find mGCH _____

32. Example 10
TVWX is a rhombus. Find TV ____ and mVTZ ___

33. G-04 Assignment
Page 395 #3 – 12, 21 – 24 ALL Page 402 #1, 2, 9, 10 Page 412 #2 – 7, 10 – 15 Study Guide (questions to circle) Page 395 #9, 11 Page 402# 1, 2, 9 Page 412 #3, 5, 6, 7