1. Properties of Parallelograms
Tutorial 13a

2. Parallelogram:
A PARALLELOGRAM ( ) is a quadrilateral with two pairs of parallel sides.
For example: A B D C

3. Parallelogram:
A PARALLELOGRAM ( ) is a quadrilateral with two pairs of parallel sides. A D
AD BC
AB CD
is a symbol for a
“Parallelogram” C B
ABCD

4. Parallelogram:
Terms to know:
Opposite sides A D C B

5. Parallelogram:
Terms to know:
Opposite sides AB & DC A D C B

6. Parallelogram:
Terms to know:
Opposite sides AB & DC ; AD & BC A D C B

7. Parallelogram: A C Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C A D C B

8. Parallelogram: D B Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D D A B C

9. Parallelogram: A B Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
Consecutive angles A & B; A D B C

10. Parallelogram: C B Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
Consecutive angles A & B; B & C A D C B

11. Parallelogram: D C Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
Consecutive angles C & D; D A C B

12. Parallelogram: A D Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
Consecutive angles C & D ; A & D A D C B

13. Parallelogram: Terms to know: Opposite sides AB & DC ; AD & BC
Opposite angles A & C ; B & D
Consecutive angles C & D ; A & D
Diagonals AC & BD A A D D C B B C

14. Properties of Parallelograms
Opposite sides are parallel A D
AD BC
AB CD C B

15. Properties of Parallelograms
Opposite sides are parallel
Opposite sides are congruent A D C B

16. Properties of Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent A D C B

17. A B Properties of Parallelograms Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary A D B C

18. Properties of Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary A D C B

19. Properties of Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
The Diagonals bisect each other A D E C B

20. Properties of Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
The Diagonals bisect each other A D E C B

21. Parallelograms Find the lengths of AB and DC in ABCD:
3x - 10
2x + 1
HELP B C
AB = CD
3x - 10 = 2x + 1
x - 10 = 1
x = 11
AB = 3x - 10 = 3(11) - 10 = 23
AB = CD = 23

22. Parallelograms Find the measures of all four angles of RSTU :3x
HELP
2x + 10 S T

23. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180

24. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180

25. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180
5x + 10 = 180

26. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180
5x + 10 = 180
5x = 170

27. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180
5x + 10 = 180
5x = 170
x = 34

28. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180
5x + 10 = 180
5x = 170
x = 34
m R = m T = 3x = 3(34) = 102

29. Parallelograms Find the measures of all four angles of RSTU :3x
2x + 10 S T
m R + m S = 180
3x + 2x + 10 = 180
5x + 10 = 180
5x = 170
x = 34
m R = m T = 3x = 3(34) = 102
m S = m U = 2x + 10 = 2(34) + 10 = 78

30. Properties of Parallelograms
Summary:
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
The Diagonals bisect each other

31. The End
Time to move on
to the assignment or
the next lesson

32. Review: Properties of Parallelograms
Summary:
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
The Diagonals bisect each other
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