1. Lesson:
6.1 Parallelograms
Pages:
291 – 294
Objectives:
To Identify the PROPERTIES of QUADRILATERALS
To Recognize and Apply the 5 PROPERTIES of a
PARALLELOGRAM

2. Geometry 6.1
A QUADRILATERAL is
Four-Sided POLYGON

3. Geometry 6.1
A QUADRILATERAL is
Four-Sided POLYGON
Remember: A POLYGON
Is a Closed Figure
Has Sides with Common Endpoints that are
NOT Collinear (Unique Sides)
Has Sides the INTERSECT exactly 2 Other Sides
at their ENDPOINTS.

4. D A C B
Name:
Adjacent sides
Opposite sides
Diagonals
Consecutive angles
Opposite Angles

6. Geometry 6.1
DEFINITION:
A PARALLELOGRAM is a Quadrilateral for which
BOTH Pairs of Opposite Sides are PARALLEL.
ABCD means parallelogram ABCD.

7. Geometry 6.1 D C
Draw B A

8. Geometry 6.1
THEOREM – OPPOSITE SIDES of a Parallelogram
are CONGRUENT.

9. D C
What is TRUE about
CONSECUTIVE Angles? B A

10. THEOREM – CONSECUTIVE ANGLES of a Parallelogram
are SUPPLEMENTARY.

11. Geometry 6.1 D C
If Opposite Sides are
PARALLEL and CONGRUENT,
What is TRUE about
OPPOSITE ANGLES? B A

12. THEOREM – OPPOSITE ANGLES of a Parallelogram
are CONGRUENT.

13. DEFINITION:
A Diagonal is a SEGMENT that
CONNECTS
Any Two NONConsecutive Vertices.

14. Geometry 6.1 D C E B A
What is the result of Intersecting Diagonals?

15. THEOREM – The DIAGONALS of a Parallelogram
BISECT Each Other.

16. D C E A B
If AE = 5, AC = _______
If BD = x + y, BE = _______
If BE = 24, EC = ________
If EC = t, AC = ________

17. EFGH
Angle E = 9x - 3
Angle G = 8x + 6
Angle E = ?

18. MTRA
MA = 7
Angle M = 65
TR =
Angle T =

19. Geometry 6.1
Quadrilaterals & Parallelograms D C F E A B
ABCD with
Given:
Prove:

20. Geometry 6.1
Quadrilaterals & Parallelograms
SUMMARY of Properties of a Parallelogram
OPPOSITE Sides of a Parallelogram are PARALLEL
OPPOSITE Sides of a Parallelogram are CONGRUENT
OPPOSITE Angles of a Parallelogram are CONGRUENT.
CONSECUTIVE Angles of a Parallelogram are
SUPPLEMENTARY
DIAGONALS of a Parallelogram BISECT each other.

21. ABCD is a Parallelogram15 C Yo Wo
55o Zo x B A
Find the values of x, y, and z.

22. W 2c X
WXYZ is a Parallelogram
What are a,b,c and d. 15 a= b= c= d= a
18o Z
31o 22 Y

23. In Parallelogram ABCD,
Find the measures of angles, A, B, C, and D

24. If RQ = 5x + 1 and QT = 3x + 15 Find QT In Parallelogram RSTV,
Diagonals RT and VS intersect at Q.
If RQ = 5x + 1
and
QT = 3x + 15
Find QT

25. A B
GIVEN: 1
PROVE: D E C

26. Geometry 6.1
You should be able to:
Use PROPERTIES to Identify a QUADRILATERAL
List the PROPERTIES of a PARALLELOGRAM
Use Parallelogram Properties to SOLVE Problems