Day 8 ­Section 6.4.notebook
January 17, 2014
DIRT
1. Solve for the variable:
a. 8x­3=6x+5
b. 4(2y+1) = 20
2. Re­write the following equation in slope­intercept 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
Day 8 ­Section 6.4.notebook
January 17, 2014
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
G.1.A
Performance 3.4 DOK­2
2
Day 8 ­Section 6.4.notebook
January 17, 2014
5 ways to prove that a quadrilateral is a parallelogram: What is the word behind the box? 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
3
Day 8 ­Section 6.4.notebook
January 17, 2014
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******
4
Day 8 ­Section 6.4.notebook
January 17, 2014
Rhombus­ equilateral parallelogram­­properties in addition to the ones listed above.
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
2
4
5
2)
50
4
1
2 3
5
Day 8 ­Section 6.4.notebook
3)
January 17, 2014
4y
2x
20
16
4)
3x+1
2y­2
120
14
10
5)
6
Day 8 ­Section 6.4.notebook
January 17, 2014
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.
7
Day 8 ­Section 6.4.notebook
January 17, 2014
Assignment: p 315 #2­20 E, 48, 49, 50
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=_________
8. Draw picture and label:
6. Draw picture and label:
work:
work:
m<1=_______ m<2=________ m<3=________
m<1=_______ m<2=________ m<3=________ m<4=_________
10. Draw the rectangle and label with given information:
12. Draw the rectangle and label with given information:
work: work: x=______ LN=______ MP=_______
x=______ LN=______ MP=_______
8
Day 8 ­Section 6.4.notebook
January 17, 2014
14. Draw the rectangle and label with given information:
16. Is the quadrilateral a parallelogram? ______
Explain why: ______________________________________________
18. Is the quadrilateral a parallelogram? _______
work: Explain why: _______________________________________________
20. Is the quadrilateral a parallelogram? ________
Explain why: ______________________________________________
x=______ LN=______ MP=_______
48. Draw the figure:
49. Draw the figure:
50. Draw the figure:
work: work: work: x=___________
x=________ y=_______ z=________
x=________ y=_______ 9