Download 6.4 Special Parallelogram 2.notebook

6.4 Special Parallelogram 2.notebook
January 07, 2015
DIRT
1. Solve for the variable:
a. 8x­3=6x+5
b. 4(2y+1) = 20
2. Re­write the following equation in slope­ intercept form: 2y + 7 = x
3. What does it mean if two lines are perpendicular? Explain using words. Then, draw and label a picture of two perpendicular lines. 1
6.4 Special Parallelogram 2.notebook
January 07, 2015
6.4 Special Parallelograms
Objectives: ­ To use properties of diagonals of rhombus or rectangle
­ To determine whether a parallelogram is a rhombus, or a rectangle
Review:
5 ways to prove that a quadrilateral is a parallelogram: 1) Opposite sides are parallel
2) Opposite sides are congruent
3) Opposite angles are congruent
4) Diagonals bisect each other
5) One set of sides are both parallel and congruent
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6.4 Special Parallelogram 2.notebook
January 07, 2015
2 ways to prove that a parallelogram is a RECTANGLE: 1) One right angle in the corner
2) Diagonals are congruent
2 ways to prove that a parallelogram is a RHOMBUS: 1) Consecutive sides are congruent
2) Diagonals are perpendicular (Rt angle in the middle)
*****The diagonals of a rhombus bisect the angles******
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6.4 Special Parallelogram 2.notebook
January 07, 2015
Rhombus­ equilateral parallelogram­­all properties of a parallelogram apply and
1) All 4 sides are congruent
2) Diagonals are perpendicular bisectors
3) Each diagonal bisects 2 angles
Code and label the picture
Examples: Find the measures of the numbered angles in each rhombus (code and label the pictures)
1)
120
3
1
4
2
5
2)
50
4
1
2 3
4
6.4 Special Parallelogram 2.notebook
3)
January 07, 2015
4y
2x
20
16
4)
2y­2
3x+1
120
14
10
5)
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6.4 Special Parallelogram 2.notebook
January 07, 2015
One diagonal of a rectangle has length 8x + 2. The other diagonal has length 5x + 11. Find the length of each diagonal
The diagonals of ABCD are perpendicular. AB = 16 cm and BC = 8 cm. Can ABCD be a parallelogram? Explain.
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