L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a...
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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?
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Transcript of L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a...
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?
Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 6 – 9: Rhombus Diagonals Bisect Angles.
The diagonals of a rhombus are perpendicular.
Theorem 6 – 10: Rhombus Diagonals are Perpendicular.
MNPQ is a rhombus and Find the measure of the numbered angles.
Example 1: Finding Angle Measures.
.120Nm
Find the measures of the numbered angles in the rhombus below.
The diagonals of a rectangle are congruent.
Theorem 6 – 11: Diagonals of a Rectangle.
Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y – 5.
Example 2: Finding Diagonal Length.
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.
If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.
Theorem 6 – 12:
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6 – 13:
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Theorem 6 – 14:
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.
Example 3: Recognizing Special Parallelograms.
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.
Example 4: Real-World Connection.
Pgs. 315-317 #s 2 – 20 even, 48 – 50 all.
Homework:
