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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<P + m<Q = 180°

    m<Q + m<R = 180°

    m<R + m<S = 180°

    m<S + m<P = 180°

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

<KJM

N

<LMJ

NL

MJ

J

M


Find the measure in parallelogram lmnq
Find the measure in parallelogram LMNQ.

  • LM

  • LP

  • LQ

  • QP

  • m<LMN

  • m<NQL

  • m<MNQ

  • m<LMQ

18

8

L

M

9

110°

10

10

9

P

70°

8

32°

70 °

Q

N

18

110 °

32 °


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