Transcript 6.2 Properties of Parallelograms

6.2 Properties of Parallelograms
• A parallelogram is a quadrilateral with both
pairs of opposite sides parallel.
• In a quadrilateral, opposite sides do not share
a vertex and opposite angles do not share a
side.
Theorem 6.3
• If a quadrilateral is a parallelogram, then its
opposite sides are congruent.
Consecutive Angles
• Angles of a polygon that share a side are
consecutive angles.
Theorem 6.4
• If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary.
Using Consecutive Angles
•
A.
B.
C.
D.
What is the measure of angle P in parallelogram
PQRS?
26°
64°
116°
126°
mP  mS  180
mP  64  180
mP  116
Theorem 6.5
• If a quadrilateral is a parallelogram, then its
opposite angles are congruent.
Theorem 6.6
• If a quadrilateral is a parallelogram, then its
diagonals bisect each other.
Using Algebra to Find Lengths
• Solve a system of linear equations to find the
values of x and y in parallelogram KLMN. What
are KM and LN?
Using Algebra to Find Lengths
KP  MP
LP  NP
y  10  2 x  8
x  y2
y  10  2( y  2)  8
y  10  2 y  4  8
10  y  4
14  y
x  14  2
x  16
KM  2( KP)
KM  2( y  10)
 2(14  10)
 48
LN  2( LP)
LN  2 x
 2(16)
 32
Theorem 6.7
• If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off
congruent segments on every transversal.
Using Parallel Lines and Transversals
• In the figure, AE || BF || CG || DH, AB = BC = CD = 2,
and EF = 2.25. What is EH?
EF = FG = GH
EH = EF + FG + GH
EH = 2.25 + 2.25 + 2.25
EH = 6.75
More Practice!!!!!
• Homework – p. 364 - 365 #9 – 12, 14 –
27, 29 – 30 ALL.