Properties of Parallelograms Ch 6-2

Parallelogram or //ogram or Definition: A quadrilateral with opposite sides parallel.

1 2 4 3 5 6 8 7 2  4 Corr  Thm 4  7 Alt. Int.  Thm 2  7 Trans. Prop.  6  8 Corr  Thm 8  3 Alt. Int.  Thm 6  3 Trans. Prop. 

//ograms  Opposite s are 

1 5 6 2 3 7 4 8 1 and 2 are Supp. Linear Pair Thm 1  3 Corr.  Thm 2 and 3 are Supp. Substitution or Consec. Int.  Thm

//ograms  Consecutive angles are supplementary. Q T S R mQ + mR = 180o mR + mS = 180o mS + mT = 180o mT + mQ = 180o

If a parallelogram has one right angle, then it has four right angles. Not on vocab sheet! If a parallelogram has one right angle, then it has four right angles.

Corr. Parts of  figures are  B 1 3 4 2 C D 1  2 Opposite  are  3  4 Alt. Int.  Thm Reflexive Prop.  ABC  DCB AAS   Thm Corr. Parts of  figures are 

Parallelograms  Opposite sides are 

Corr. Parts of  figures are  B D C E ABE  DCE Alt. Int.  Thm BAE  CDE Alt. Int.  Thm AB  CD Opposite sides  ABE  DCE ASA   Thm AE  DE CE  BE Corr. Parts of  figures are  E is the midpoint of AD and CB Def of Midpt.

//ograms  Diagonals bisect each other.

ACD  CAB Diagonals of a parallelogram separates the parallelogram into two congruent triangles. ACD  CAB A B C D

ABCD is a parallelogram. Find x. 4 5 8 20 A B C D

ABCD is a parallelogram. Find mBCD. 54 64 62 58

ABCD is a parallelogram. Find mBDC. 54 64 62 58 A B C D

Homework Chapter 6-2 Pg 328: # 3-11, 13proof, 15-30, 46-49