1. 6-5: Conditions of Special Parallelograms
Page 432
14)
58°
15)
𝟏𝟐𝟐°
16)
𝟓𝟐°
17)
62°
18)
96.6
19)
+𝟒 𝟓
20)
2.8
21)
3.6
22)
72.5
23)
Sometimes
24)
25)
Never
27)
𝒎∠𝟏=𝟖𝟐°
𝒎∠𝟐=128°
28)
𝒎∠𝟏=116°
𝒎∠𝟐=46°
29)
𝒎∠𝟏=𝟓𝟏°
𝒎∠𝟐=16°
30)
𝒎∠𝟏=112°
𝒎∠𝟐=40°
31)
𝒎∠𝟏=120°
32)
𝒎∠𝟏=117°
34) 15
35) 13
36) 8
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6-5: Conditions of Special Parallelograms

2. 6-5: Conditions of Special Parallelograms
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6-5: Conditions of Special Parallelograms

3. Quadrilaterals in Coordinate Plane
Section 6-6A
Geometry PreAP, Revised ©2013
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6-5: Conditions of Special Parallelograms

4. Types of Quadrilaterals
Parallelogram
Rhombus
Rectangle
Square
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6-5: Conditions of Special Parallelograms

5. Graphing Quadrilaterals
Establish all four points
Opposite sides measure the same slope
Calculate the side lengths using the distance formula
Calculate the slope and distance of the diagonals
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6-5: Conditions of Special Parallelograms

6. 6-5: Conditions of Special Parallelograms
Example 1
Four vertices of ABCD are A(3, –8), B(–2, 2), C(2, 6) and D(7, –4). Identify the shape, slope of AB, CD, AD, BC, the distances, and slopes of the diagonals, and distances of them. A B C D
2/15/ :07 PM
6-5: Conditions of Special Parallelograms

7. 6-5: Conditions of Special Parallelograms
Example 1
Four vertices of ABCD are A(3, –8), B(–2, 2), C(2, 6) and D(7, –4). Identify the shape, slope of AB, CD, AD, BC, the distances, and slopes of the diagonals, and distances of them. A B C D
2/15/ :07 PM
6-5: Conditions of Special Parallelograms

8. 6-5: Conditions of Special Parallelograms
Example 1
Four vertices of ABCD are A(3, –8), B(–2, 2), C(2, 6) and D(7, –4). Identify the shape, slope of AB, CD, AD, BC, the distances, and slopes of the diagonals, and distances of them. A B C D
2/15/ :07 PM
6-5: Conditions of Special Parallelograms

9. 6-5: Conditions of Special Parallelograms
Example 1
Four vertices of ABCD are A(3, –8), B(–2, 2), C(2, 6) and D(7, –4). Identify the shape, slope of AB, CD, AD, BC, the distances, and slopes of the diagonals, and distances of them. A B C D
2/15/ :07 PM
6-5: Conditions of Special Parallelograms

10. 6-5: Conditions of Special Parallelograms
Example 2
Four vertices of ABCD are A(–1, 0), B(–3, 5), C(2, 7) and D(4, 2). Identify the shape, slope of AB, CD, AD, BC, the distances, and slopes of the diagonals, and distances of them.
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6-5: Conditions of Special Parallelograms

11. 6-5: Conditions of Special Parallelograms
Your Turn
Four vertices of FGHJ are F(–4, –2), G(–2, 2), H(4, 3) and J(2, –1). Identify the shape, slope of FG, GH, HJ, FJ, the distances, and slopes of the diagonals, and distances of them.
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6-5: Conditions of Special Parallelograms

12. 6-5: Conditions of Special Parallelograms
Example 3
Given the quadrilateral JKLM, the slope of JK and LM is –5/3. The slope of KL and MJ is ¾. What shape is it?
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6-5: Conditions of Special Parallelograms

13. 6-5: Conditions of Special Parallelograms
Assignment
Worksheet
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6-5: Conditions of Special Parallelograms