6.2 Properties of Parallelograms

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6.2 Properties of Parallelograms

• Chapter 6
• Quadrilaterals

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6.2 Properties of Parallelograms

• Theorem 6-1
• Opposite sides of a parallelogram are congruent

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Consecutive and Opposite Angles

• Consecutive Angles Angles that share a side
  (Angles that are next to each other)
• Opposite Angles Angles that are across from
  each other in the parallelogram

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6.2 Properties of Parallelograms

• Consecutive Angles are Supplementary because they
  are same-side interior angles

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Using Consecutive Angles

• Find mltS in RSTW

ST and RW are parallel, so ltS and ltR are what
kind of angles?
S
T
68
W
R
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6.2 Properties of Parallelograms

• Theorem 6-2
• Opposite angles of a parallelogram are
  congruent

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Using Algebra

• Find the value of x in PQRS. Then find QR
  and PS.

3x - 15
R
Q
S
P
2x 3
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Using Algebra

• Find the value of y in EFGH. Then find mltE,
  mltF, mltG, mltH.

E
F
3y 37
6y 4
G
H
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6.2 Properties of Parallelograms

• Theorem 6-3
• The diagonals of a parallelogram bisect each
  other

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Using Algebra

• Solve the system of equations to find the values
  of x and y.

B
C
x 1
2x
3y - 7
y
D
A
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Solve
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Using Algebra

• Solve the system of equations to find the values
  of x and y. Then find AE, EC, BE, and ED.

B
C
x 1
2x
E
3y - 7
y
D
A
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Using Algebra

• Find the values of a and b.

X
Y
a
2a - 8
V
b 10
b 2
Z
W
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Theorem 6-4

• Theorem 6-4
• If three (or more) parallel lines cut off
  congruent segments on one transversal, then they
  cut off congruent segments on every transversal.

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Measurement

• In the figure, DH ll CG ll BF ll AE, and AB BC
  CD 2, and EF 2.5. Find EH.

H
D
2
G
C
2
F
B
2
2.5
A
E
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Practice

• Pg 297 1-21, 24-33