6 – 4 Special Parallelograms
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?

Theorem 6 – 9: Rhombus Diagonals Bisect Angles.
Each __________________ of a rhombus _______________ two
angles of the __________________.

Theorem 6 – 10: Rhombus Diagonals are Perpendicular.
The ____________________ of a ___________________ are
____________________________.
Example 1: Finding Angle Measures.
- 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.
Theorem 6 – 11: Diagonals of a Rectangle.
The ________________ of a ________________________ are
___________________.
Example 2: Finding Diagonal Length.
- Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y – 5.
-
Find the length of the diagonals of GFED if FD = 5y - 9 and GE = y + 5.
Theorems Used to Prove Whether a Parallelogram is a Rhombus or a Rectangle.

Theorem 6 – 12:
If one __________________ of a parallelogram _________________ two _____________ of the
parallelogram, then the parallelogram is a __________________.

Theorem 6 – 13:
If the __________________ of a parallelogram are __________________________, then the
parallelogram is a ___________________.

Theorem 6 – 14:
If the ______________________ of a parallelogram are _____________________, then the
parallelogram is a _____________________.
Example 3: Recognizing Special Parallelograms.
- Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain.
o The quadrilateral has congruent diagonals and one angle of 60 degrees.
o 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.
Example 4: Real-World Connection.
- 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.
Homework: pgs. 315 – 317 #s