Special Parallelograms: Properties and Examples
Learn about the properties and characteristics of rhombuses and rectangles, and how to determine if a parallelogram is a rhombus or a rectangle. Explore the theorems related to diagonals, angle measures, and special parallelograms through examples and exercises. Get insights on recognizing special parallelograms with congruent or perpendicular diagonals. Homework practice included!
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Presentation Transcript
6-4 SPECIAL PARALLELOGRAMS M11.C.1 2.9.11.C Objectives: 1) To use properties of diagonals of rhombuses and rectangles 2) To determine whether a parallelogram is a rhombus or a rectangle
THEOREMS Each diagonal of a rhombus bisects two angles of the rhombus The diagonals of a rhombus are perpendicular.
EXAMPLE: FINDING ANGLE MEASURES MNOP is a rhombus. Angle N is 120. Find the measure of the numbered angles
EXAMPLE: PAGE 313 Find the measure of the numbered angles.
THEOREM The diagonals of a rectangle are congruent.
EXAMPLE: FINDING DIAGONAL LENGTH Rectangle ABCD BD = 2y + 4 AC = 6y - 5
THEOREMS 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.
RECOGNIZING SPECIAL PARALLELOGRAMS Determine whether the quadrilateral can be a parallelogram. If not, write impossible. The quadrilateral has congruent diagonals and one angle of 60 degrees. The quadrilateral has perpendicular diagonals and four right angles. 1. 2. 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. 3.
Homework Page 315 #1-21
