1. 6-4: Properties of Special Parallelograms
Page 395
15)
82.9
16)
110
17)
18)
50°
19)
130°
20)
21) 10
22) 20
23) 28
24) 14
32)
∠𝑹𝑲𝑴
33)
∠𝑲𝑴𝑷
34) 𝑹𝑻
35) 𝑲𝑴
36) 𝑹𝑲
37) 𝑹𝑷
38)
∠𝑹𝑲𝑷
39)
∠𝑹𝑻𝑷
40)
180°
41)
x = 119, y = 61, z = 119
42)
x = 90, y = 37, z = 53
43)
x = 24, y = 50, z = 50
46)
x = 3, y = 6
47)
x = 5, y = 8
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6-4: Properties of Special Parallelograms

2. 6-4: Properties of Special Parallelograms
Page 402
11)
Yes, all sides are congruent to each other
12)
Yes, Each pair of angles are alternate interior angles
13) No
14)
JK and LM’s Slope is –7/2; KL and MJ = -1/5
15)
JK and LM’s Slope is –7/2; KL and MJ = −1/5
20)
A = 16, b = 14
21)
A = 16.5, b = 23.2
22)
A = 7.25, b = 6.5
23)
A = 8.4, b = 20
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6-4: Properties of Special Parallelograms

3. 6-4: Properties of Special Parallelograms

4. Properties of Special Parallelograms
Section 6-4
Geometry PreAP, Revised ©2013
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6-4: Properties of Special Parallelograms

5. Properties of Rectangles
If a quadrilateral is a rectangle, then it is a parallelogram
If a parallelogram is a rectangle, then its diagonals are congruent
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6-4: Properties of Special Parallelograms

6. 6-4: Properties of Special Parallelograms
Rhombus
A. A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.
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6-4: Properties of Special Parallelograms

7. 6-4: Properties of Special Parallelograms
Properties of Rhombus
If a quadrilateral is a rhombus, then it is a parallelogram
If a parallelogram is a rhombus, then its diagonals are perpendicular
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles
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6-4: Properties of Special Parallelograms

8. 6-4: Properties of Special Parallelograms
Rhombus
A. A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.
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6-4: Properties of Special Parallelograms

9. 6-4: Properties of Special Parallelograms
Squares
A square is a regular parallelogram.
All angles are congruent
All sides are congruent
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6-4: Properties of Special Parallelograms

10. 6-4: Properties of Special Parallelograms
Shapes
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6-4: Properties of Special Parallelograms

11. 6-4: Properties of Special Parallelograms
Example 1
TVWX is a rhombus. Find TV.
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6-4: Properties of Special Parallelograms

12. 6-4: Properties of Special Parallelograms
Example 2
CDFG is a rhombus. Solve for mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)°
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6-4: Properties of Special Parallelograms

13. 6-4: Properties of Special Parallelograms
Your Turn
Find the length of diagonal in a rectangle of ABCD if AC = 2(5a + 1) and BD = 2(a + 1).
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6-4: Properties of Special Parallelograms

14. 6-4: Properties of Special Parallelograms
Example 3
In the figure, a small square is inside a larger square. What is the area, in terms of x, of the shaded region?
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6-4: Properties of Special Parallelograms

15. 6-4: Properties of Special Parallelograms
Assignment
Pg 412: 10-15, all
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6-4: Properties of Special Parallelograms