6.2 Properties of Parallelograms

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# 6.2 Properties of Parallelograms - PowerPoint PPT Presentation

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

m

m

m

m

Q

R

S

P

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
• PQRS is a parallelogram. Find the value of h.

P

Q

3h

120°

S

R

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

R

Q

M

P

S

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

5

5

F

G

3

3

K

J

H

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.
• 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 °