Transcript GEOMETRY Section 6.3: Conditions for a Parallelogram

BASIC GEOMETRY
Section 6.3: Conditions for a Parallelogram
Properties & Conditions
 Properties
 If it is a parallelogram, then it does this
 yesterday
 Conditions
 If it does this, then it is a parallelogram
 Today
6 Conditions to make a parallelogram
 If any one of these sets of conditions, then the figure must be
a parallelogram
 Def of parallelogram
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1 pair of  & sides 
Both pair of opposite sides = 
Both pair of opposite angles = 
 supp to both its cons 's 
Diags bisect each other 
Example 1
Show that JKLM is a parallelogram for a = 3 & b = 9.
Example 2
Show that PQRS is a parallelogram for x = 10 & y = 6.5.
Example 3
Determine if each quadrilateral must be a parallelogram. Justify
your answer.
Example 4
Show that quadrilateral JKLM is a parallelogram by using the def
of parallelogram.
J(-1,-6), K(-4,-1), L(4,5), M(7,0);
Example 5
Show that quadrilateral ABCD is a parallelogram by one pair of
opp sides // and =.
A(2,3), B(6,2), C(5,0), D(1,1)
Example 6
The legs of a keyboard tray are connected by a bolt at their
midpoints, which allows the tray to be raised or lowered.
Why is PQRS always a parallelogram?
Assignment #3 page 402 #’s 1-8,35-37,(46)