6 2 properties of parallelograms
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6.2 Properties of Parallelograms

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6.2 Properties of Parallelograms. Theorems. If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. Q. R. S. P. Theorems.

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theorems
Theorems
  • If a quadrilateral is a parallelogram, then its opposite sides are congruent.
  • If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Q

R

S

P

theorems1
Theorems
  • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

m

m

m

m

Q

R

S

P

using properties of parallelograms
Using Properties of Parallelograms
  • PQRS is a parallelogram. Find the angle measure.
    • m< R
    • m< Q

Q

70 °

R

70 ° + m < Q = 180 °

m< Q = 110 °

70°

P

S

using algebra with parallelograms
Using Algebra with Parallelograms
  • PQRS is a parallelogram. Find the value of h.

P

Q

3h

120°

S

R

theorems2
Theorems
  • If a quadrilateral is a parallelogram, then its diagonals bisect each other.

R

Q

M

P

S

using properties of parallelograms1
Using properties of parallelograms
  • FGHJ is a parallelogram. Find the unknown length.
    • JH
    • JK

5

5

F

G

3

3

K

J

H

examples
Examples
  • Use the diagram of parallelogram JKLM. Complete the statement.

LM

K

L

NK

N

NL

MJ

J

M

find the measure in parallelogram lmnq
Find the measure in parallelogram LMNQ.
  • LM
  • LP
  • LQ
  • QP
  • m
  • m
  • m
  • m

18

8

L

M

9

110°

10

10

9

P

70°

8

32°

70 °

Q

N

18

110 °

32 °

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