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6.2 Parallelograms
Check.3.2 , Connect coordinate geometry to geometric
figures in the plane (e.g. midpoints, distance formula, slope,
and polygons).
Check.4.10 , Identify and apply properties and relationships
of special figures (e.g., isosceles and equilateral triangles,
family of quadrilaterals, polygons, and solids).
Spi.3.2 Use coordinate geometry to prove characteristics of
polygonal figures.
Copy the following into your notes:
Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A
B
C
D
Properties of Parallelogram
Opposite Sides of a parallelogram are congruent
Opposite Angles of a parallelogram are congruent
Consecutive Angles of a parallelogram are supplementary.
mA+ mB = 180, mB+ mC = 180
mC+ mD = 180, mD+ mA = 180
If a parallelogram has 1 right angle, it has 4 right angles
Objective: To understand and be able to apply properties of sides, angles and diagonals
of parallelograms.
Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
B
A
C
D
Properties of Parallelogram
Diagonals of a parallelogram bisect each other
Each Diagonal of a parallelogram separates the
parallelogram in to two congruent Triangles
Applying Properties
• Quadrilateral LMNP is a parallelogram.
– Find mPLM, mLMN, and d.
•
•
•
•
mPNM = 66 + 42 = 108 by angle addition
mPNM = mPLM Opposite angles of parallelogram are 
mPLM = 108 Substitution
mPL M + mLMN = 180, Consecutive Angles of
parallelograms are supplementary.
• 108 + mLMN = 180, substitution
• mLMN = 72
• LM  PN, opposite sides of Parallelogram are congruent
• 2d = 22
• D = 11
Solve
3y = 18
y=6
URT = 40
UTS = 18+40 = 58
UTS = URS = 58
UTS + RST = 180
58 + RST = 180
RST = 122
Diagonals of Parallelogram
• What are the coordinates of the intersection of
the diagonals of a parallelogram ABCD with
vertices A(2, 5), B(6,6), C(4,0) and D(0, -1)?
• Diagonals of parallelogram bisect each other.
Summary
• Parallelograms have
– Opposite sides are parallel and congruent
– Opposite angles are congruent
– Consecutive angles are supplementary
– Diagonals bisect each other
• Practice Assignment
• Block Page 404, 10 - 22 Even