Download Chapter 5 Theorems Geometry AC Name Theorem 5

Chapter 5 Theorems
Geometry AC
Name _______________________
Theorem 5-1 If a quadrilateral is a parallelogram then the opposite sides are congruent.
(Opposite sides of a parallelogram are congruent.)
Given:
EFGH
H
G
Prove: EF  GH
E
STATEMENTS
REASONS
F
Theorem 5-2 If a quadrilateral is a parallelogram then the opposite angles are congruent.
(Opposite angles of a parallelogram are congruent.)
Given:
PQRS
Q
R
Prove: P  R ; Q  S
P
STATEMENTS
REASONS
S
Theorem 5-3 If a quadrilateral is a parallelogram then the diagonals bisect each other.
(The diagonals of a parallelogram are bisect each other.)
Given:
QRST
T
Prove: QS bisects RT; RT bisects QS
3
M
4
Q
STATEMENTS
1
REASONS
2
R
S
Theorem 5-4 If BOTH pairs of opposite sides of a quadrilateral are congruent, then it is a
parallelogram.
Given: TS  QR; TQ  SR
Prove:
T
S
QRST
Q
STATEMENTS
REASONS
R
Theorem 5-5 If ONE PAIR of opposite sides is BOTH parallel and congruent, then the
quadrilateral is a parallelogram.
Given: WZ || XY; WZ  XY
Prove:
Z
Y
WXYZ
W
STATEMENTS
REASONS
X
Theorem 5-6 If BOTH PAIRS of opposite angles are congruent, then the quadrilateral is a
parallelogram.
Given: L  N ; M  O
Prove:
O
N
LMNO
L
STATEMENTS
REASONS
M
Theorem 5-7 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a
parallelogram.
Given: HJ bisects KI; KI bisects HJ
Prove:
K
HIJK
M
H
STATEMENTS
J
REASONS
I