Download Honors Geometry Section 4.5 (1) Parallelograms

Honors Geometry Section 4.5 (1)
Parallelograms
A parallelogram is a quadrilateral
with both pairs of opposite sides
parallel.
To name the parallelogram to the
right, we use the notation
You will need to know the
following properties of
parallelograms.
Theorem 4.5.2
In a parallelogram, opposite sides are
congruent
1) Quad. MWEO is a parallelogram
1) Given
2) Draw ME
2) Though any 2 points
there is exactly one line
3) MW // OE , MO // WE
3) Def. of Parallelogram
4) WME & MEO are AIAs
WEM & EMO are AIAs
4) Def. of AIAs
5) WME  MEO
WEM  EMO
5) AIAT
6) ME  ME
6) Reflexive Prop.
)WME  OEM
7) ASA
) MW  OE , MO  WE
) CPCTC
Theorem 4.5.3
In a parallelogram, opposite angles are
congruent
Theorem 4.5.4
In a parallelogram, consecutive angles
are supplementary.
Theorem 4.5.5
In a parallelogram, the diagonals
bisect each other.
1) Quad. HWOL is a parallelogram
2) HL // WO
1) Given
2) Def. of //gram
3) SHL & SOW are AIAs
SLH & SWO are AIAs
3) Def of AIAs
4) SHL  SOW
SLH  SWO
4) AIAT
5) HL  WO
5) In a //gram, opp. sides 
) HSL  OSW
) WS  SL, HS  SO
5) ASA
) CPCTC
1. Name all congruent segments.
NI  HE, NH  IE
NG  GE, GH  IG
2. Name all congruent angles.
GNH  GEI
GHN  GIE
GHE  GIN
GEH  GNI
NGI  HGE
NGH  EGI
NHE  NIE
INH  HEI
3 x  5  6 x  11
16  3 x
x  16
3
2(3 y  11)  8 y
6 y  22  8 y
22  2 y
y  11
3 z  5  6 z  11  180
9 z  6  180
9 z  186
z  20. 6
6 w  5  13w  11
16  7 w
w  16
7