Download Notes 6-4 - Robinson Schools

SB En Geom 6­4 Completed.notebook
Lesson 6­4
October 17, 2012
Special Parallelograms
If you draw a diagonal in a rhombus, what kind of triangles are formed?
Thm 6­9
Each diagonal of a rhombus bisects two angles of the rhombus.
How would you prove this?
Nov 5­8:38 AM
Thm 6­10
The diagonals of a rhombus are perpendicular.
Expl 1. Find the angle measures in the rhombus.
N
120
0
P
3
4
1
2
M
Q
Ckpt 1. Find the measures of the numbered angles in the rhombus.
500
1
4
2
3
Nov 5­8:41 AM
1
SB En Geom 6­4 Completed.notebook
October 17, 2012
Thm 6­11
The diagonals of a rectangle are congruent.
Expl 2. Find the length of the diagonal FD of rectangle GFED is FD = 2y + 4 and GE = 6y ­ 5.
F
E
G
D
Ckpt 2. Find the length of the diagonals of GFED if FD = 5y ­ 9 and GE = y + 5.
Nov 5­8:46 AM
And the converses...
Thm 6­12
If one diagonal of a parallelogram bisects the angles of the parallelogram, then the parallelogram is a rhombus.
Thm 6­13
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Thm 6­14
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Nov 5­8:49 AM
2
SB En Geom 6­4 Completed.notebook
October 17, 2012
Expl 3. Determine whether the quadrilateral can be a parallelogram. Explain.
a.
b.
A
B
AC = BD
D
C
Chpt 3. A parallelogram has angles of 30, 150, 30, and 150. Can you conclude that it is a rhombus or a rectangle? Explain.
Extra 3. A diagonal of a parallelogram bisects two angles of the parallelogram. Is it possible for the parallelogram to have sides of lengths 5, 6, 5, and 6? Explain.
Nov 5­8:52 AM
Expl 4 ­ in your book.
Ckpt 4. Is Kate right?
Nov 5­8:55 AM
3
SB En Geom 6­4 Completed.notebook
October 17, 2012
Homework
Lesson 6­4
1­20, 44­49,
50­53, 64­66
Nov 5­8:58 AM
4