Parallelograms and Polygons

Can you determine whether this figure is a parallelogram?

• Yes

• No

If DE = 4x + 7 and EB = 5x - 4 in parallelogram ABCD, write an equation that could be used to find x.

• 4x + 7 = 5x - 4

• 4x + 7 + 5x - 4 = 180

• 4x +7 +5x - 4 = 360

If DE = 4x + 7 and EB = 5x - 4 in parallelogram ABCD, Solve for x.

• x = 10

• x = 11

• x = 12

Find the sum of the measures of the interior angles of a 43-gon.

• 7380

• 7740

• 180

• 43

If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°,

and m∠BCE = 24°.

CD =

If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°,

and m∠BCE = 24°.

BD =

Reason 1: Given

Reason 2: ​ (a)  

Reason 3 and 4: ​ (b)  

Reason 5: ​ (c)  

Reason 6: ​ (d)  

Reason 7: ​ (e)  

• Definition of parallelogram

• Alternate Interior Angles

• Parallelogram diagonals bisect each other

• AAS

• CPCTC

• Alternate Interior Converse

• Definition of Bisector

• ASA

If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°,

and m∠BCE = 24°.

m∠EBD=

If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°,

and m∠BCE = 24°.

m∠EDC=

If EBCD is a parallelogram, EB = 16, ED = 25, BF = 11, EC = 34, m∠BED = 55°, m∠CDB = 67°,

and m∠BCE = 24°.

m∠DBC=