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Properties of Parallelograms

Properties of Parallelograms

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Properties of Parallelograms

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  1. Properties of Parallelograms Ch 6-2

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

  3. 1 5 2 6 3 7 4 8 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. 

  4. //ograms  Opposite s are 

  5. 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

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

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

  8. A 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 

  9. Parallelograms  Opposite sides are 

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

  11. //ograms  Diagonals bisect each other.

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

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

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

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

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