L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a parallelogram is a rhombus or a rectangle?


Each diagonal of a rhombus bisects two angles of the rhombus.


The diagonals of a rhombus are perpendicular.



MNPQ is a rhombus and m

N

120 .
Find the measure of the numbered angles.


Find the measures of the numbered angles in the rhombus below.


The diagonals of a rectangle are congruent.


Find the length of the diagonals of rectangle
GFED if FD = 2y + 4 and GE = 6y – 5.

GFED
FD
y
GE
y


If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.


If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.


If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.


Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain.
◦ The quadrilateral has congruent diagonals and one angle of 60 degrees.
◦ The quadrilateral has perpendicular diagonals and four right angles.


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.


Community Service Builders use properties of diagonals to “square up” rectangular shapes like building frames and playing-field boundaries. Suppose you are on the volunteer building team at the right. You are helping to lay out a rectangular patio. Explain how to use properties of diagonals to locate the four corners.


Pgs. 315-317 #s 2 – 20 even, 48 – 50 all.