Download 6.4 Special Parallelogram 2 .notebook

6.4 Special Parallelogram 2 .notebook
December 08, 2014
DIRT
1. Solve for the variable:
b. 4(2y+1) = 20
a. 8x­3=6x+5
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. Dec 8­7:57 AM
Jan 14­7:16 AM
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
2 ways to prove that a parallelogram is a RECTANGLE: 1) One right angle in the corner
Review:
2) Diagonals are congruent
5 ways to prove that a quadrilateral is a parallelogram: 1) Opposite sides are parallel
2 ways to prove that a parallelogram is a RHOMBUS: 2) Opposite sides are congruent
1) Consecutive sides are congruent
3) Opposite angles are congruent
2) Diagonals are perpendicular (Rt angle in the middle)
4) Diagonals bisect each other
*****The diagonals of a rhombus bisect the angles******
5) One set of sides are both parallel and congruent
Jan 14­7:18 AM
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
Jan 14­7:22 AM
3)
4y
2x
20
Code and label the picture
16
4)
Examples: Find the measures of the numbered angles in each rhombus (code and label the pictures)
2y­2
3x+1
120
14
10
1)
120
3
1
2
4
5
5)
2)
50
4
1
2 3
Jan 14­7:23 AM
Jan 14­7:26 AM
1
6.4 Special Parallelogram 2 .notebook
One diagonal of a rectangle has length 8x + 2. The other diagonal has length 5x + 11. Find the length of each diagonal
December 08, 2014
Assignment: p 315 #2­8E, 45­47, 49, 50, 57­58, 67­69
2. Draw picture and label:
4. Draw picture and label:
work:
work:
m<1=______ m<2=_______ m<3=_______
m<1=_______ m<2=________ m<3=________ m<4=________
The diagonals of ABCD are perpendicular. AB = 16 cm and BC = 8 cm. Can ABCD be a parallelogram? Explain.
6. Draw picture and label:
8. Draw picture and label:
work:
work:
m<1=_______ m<2=________ m<1=______ m<2=______ m<3=______
m<3=________ m<4=_______
45. Good definition? _______ Why/Why not?_______________________________
46. Good definition? _______ Why/Why not?_______________________________
47. Good definition? _______ Why/Why not?_______________________________
Jan 14­7:27 AM
Jan 14­10:26 AM
49. Draw picture and label:
50. Draw picture and label:
work:
work:
x = _____ y = _____ z = _____ x = _____ y = _____ 57. Draw picture and label:
58. Draw picture and label:
work:
work:
AC= ________
BD= __________ 67. Draw picture: DB= ________
AC= ______
68. Draw picture: 69. Draw picture: Parallelogram? _______
Parallelogram? _______
Parallelogram? ______
Why/Why not?___________
Why/Why not?___________
Why/Why not?___________
_______________________
_______________________
______________________
_______________________
_______________________
______________________
Jan 14­10:30 AM
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