Understanding Special Parallelograms: Properties and Examples
Explore the properties of diagonals in rhombuses and rectangles, determine if a parallelogram is a rhombus or rectangle, and solve angle and diagonal length problems. Learn about the theorems, examples, and how to recognize special parallelograms with congruent or perpendicular diagonals. Get practice questions for better understanding.
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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
