Notes on 6-2,6-4,6-5

1. SECTION 6-2, 6-4, 6-5 3108.4.10, 4.19, 3.2
Jim Smith JCHS

2. Parallelograms are quadrilaterals with
Both pairs of opposite sides parallel.
ABCD
A B
C
D
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3. 5 Things About Parallelograms
Definition
1) Both Pairs Opp Sides Parallel
Properties
2) Both Pairs Opp Sides Congruent
3) Both Pairs Opp Angles Congruent
4) Consecutive Angles Supplementary
5) Diagonals Bisect Each Other

4. Both Pairs Opp Sides Parallel
Alternate Int Angles Are Congruent
1
2
3
4
5
6
7
8
D C
B
A
AB||DC
1 and 6
3 and 8
AD||BC
2 and 5
4 and 7

5. Both Pairs Opp Sides Congruent
23
X
42 2Y - 16
X = 23
2Y – 16 = 42
2Y = 58
Y = 29

6. Both Pairs Opposite Angles
Congruent
65°
5Y - 5
115°
X
X = 65
5Y – 5 = 115
5Y = 120
Y = 24

7. Consecutive Angles
Are Supplementary
1
2
3
4
Supplementary angles have a sum of 180

8. Diagonals Bisect Each Other
A
B C
D
X
BX = XD
AX = XC

9. 75°
80°
30°
Find The Missing Angles
In This Parallelogram
What Do You Notice About The Triangles
Formed By The Diagonals?

10. Ways To Prove Quadrilaterals
Are Parallelograms
1) Both Pairs Opp Sides Parallel
2) Both Pairs Opp Sides Congruent
3) Both Pairs Opp Angles Congruent
4) Diagonals Bisect Each Other
5 One Pair Of Sides Parallel And
Congruent

11. Determine whether ABCD is a parallelogram if
AB = 6, BC = 12, CD = 6, and DA = 12.

12. XYWZ is a quadrilateral with vertices
W(1, −4), X(-4, 2), Y(1, −1), and Z(−2, −3).
Determine if the quadrilateral is a parallelogram.

13. If the slope of PQ is −2/3 and the
slope of QR is −1/2, find the slope of SR
so that PQRS is a parallelogram
END

14. A B
C
D
1 2
3
4
5
6
7
8
9
10 11
12
Parallelogram ABCD
x
STOP

15. 5 Things About Parallelograms
Definition
1) Both Pairs Opp Sides Parallel
Properties
2) Both Pairs Opp Sides Congruent
3) Both Pairs Opp Angles Congruent
4) Consecutive Angles Supplementary
5) Diagonals Bisect Each Other

16. Rectangles Are Parallelograms
With 4 Right Angles
All 5 Things About Parallelograms
Are True…PLUS
1) All angles = 90°
2) Diagonals are congruent

17. All Angles = 90°
If 1 Angle In A Parallelogram Is A Right
Angle, Then All 4 Angles Are Right Angles
This gives us
right triangles also

18. Diagonals Are Congruent
This Gives Us 4 Congruent Segments
And 4 Isosceles Triangles
This Tells Us A Lot About The Angles

19. 1
2 3
4
5
6
7
11
12
10
9
8
Congruent Pairs of Angles

20. 1
2 3
4
5
6
7
11
12
10
9
8
Congruent Pairs of Angles

21. A Rhombus Is A Parallelogram With
4 Congruent Sides
All 5 Things About Parallelograms Are
True…PLUS
1) 4 congruent sides
2) Diagonals are perpendicular
3) Diagonals bisect opposite angles

22. 4 congruent sides
10
3Y + 1
3Y + 1 = 10
3Y = 9
Y = 3

23. Diagonal are perpendicular
A B
C
D
X
3 4
AB =
The perimeter Of
rhombus ABCD =
XC =
DB =
5
20
3
8

24. The Square Is The Most
Special Of All !!
Everything That’s True For
All The Others Is True For
Squares.

25. PARALLELOGRAMS
QUADRILATERALS
RECTANGLES RHOMBI
SQUARES