Honors Geometry
Name:__________________________
5.1 Class Notes
Date: ___________________ Period: ____
Properties of Parallelograms
Parallelogram: _____________________________________________________________________
Theorem 5-1
Opposite sides of a parallelogram are congruent.
R
T
X
U
S
Theorem 5-2
Opposite angles of a parallelogram are congruent.
Theorem 5-3
Diagonals of a parallelogram bisect each other.
Example 1:
RSTU is a parallelogram. Find the value of each variable.
R
A.
xo
yo
S
B.
R
xo
b
45o
80
S
U
C.
U
a
12
o
yo
9
43o
T
T
R
U
18
D.
22
R
2x +8
4y - 2
T
S
U
(11x)o
(4y + 5)o
o
S 80
45o
T
Example 2:
Find the perimeter of parallelogram PINE if PI = 12, and IN = 8.
Example 3:
Classify each statement as always, sometimes, or never.
A.
Parallelograms are _______________ quadrilaterals.
B.
Quadrilaterals are _______________ parallelograms.
C.
All angles of a parallelogram are _______________ congruent.
D.
All sides of a parallelogram are _______________ congruent.
E.
In parallelogram RSTU, RS is _______________ parallel to TU .
F.
In parallelogram ABCD, if mA  50 then mC _______________  130 .
G.
In parallelogram XWYZ, XY is _______________  WZ .
H.
In parallelogram ABCD, AC and BD _______________ bisect each other.
A
Given: parallelogram ABCD, and parallelogram CEFG
Prove: A  F
Statements:
1.
Parallelogram ABCD
Parallelogram CEFG
Reasons:
1.
Given
2.
2.
3.
3.
B
F
D
E
G
C
Honors Geometry
5.2 Class Notes
Name:__________________________
Date: ___________________ Period: ____
Tests for Parallelograms
Theorem 5-4: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a
parallelogram.
Theorem 5-5: If one pair of opposite sides of a quadrilateral are both parallel and congruent then the quadrilateral is
a parallelogram.
Theorem 5-6: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a
parallelogram.
Theorem 5-7: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
**By definition, if both pairs of sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
A quadrilateral is a parallelogram if any one of the following is true:
1. _____________________________________________________________________________________
2. _____________________________________________________________________________________
3. _____________________________________________________________________________________
4. _____________________________________________________________________________________
5. _____________________________________________________________________________________
Example 1: State the theorem or definition that enables you to deduce, from the information given, that quadrilateral
ABCD is a parallelogram.
B
C
A. BE = ED; CE = EA
B. BAD  DCB;
E
C. BC || AD;
AB || DC
D. BC  AD;
AB  DC
Example 2:
A
ADC  CBA
E. BC || AD;
D
BC  AD
Complete each statement with always, sometimes, or never.
A. The diagonals of a quadrilateral _______________ bisect each other.
B. If the measures of two angles of a quadrilateral are equal, then the quadrilateral is _______________ a
parallelogram.
C. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is
_______________ a parallelogram.
D. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is _______________ a
parallelogram.
E. To prove a quadrilateral is a parallelogram, it is _______________ enough to show that one pair of
opposite sides is parallel.
5.1: Pg 169 # 5-7; 20, 24, 34, 37
5.2: Pg 175 #15, 17, 20, 22, 24