1. Standard G-4 Lesson 6-5 Objectives: 1. Review of lessons 6-1, 6-2
2. To determine whether a parallelogram is a rhombus or rectangle

2. Parallelograms Rectangles
Rhombi Squares

3. › › › › › › Parallelograms Parallelograms are quadrilaterals with
Both pairs of opposite sides parallel.
ABCD › A B › › › › › D C

4. 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

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

6. Both Pairs Opp Sides Congruent23
X = 23
2Y – 16 = 42
2Y = 58
Y = 29 42
2Y - 16 X

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

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

9. Diagonals Bisect Each Other
BX = XD | || X
AX = XC || | A D

10. Diagonals are congruent
RECTANGLES
Rectangles Are Parallelograms With 4 Right Angles
All 5 Things About Parallelograms
Are True…PLUS
All angles = 90°
Diagonals are congruent

11. 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

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

13. Congruent Pairs of Angles2 3 1 4 11 9 10 12 8 5 7 6

14. Congruent Pairs of Angles2 3 1 4 11 9 10 12 8 5 7 6

15. Diagonal are perpendicular Diagonals bisect opposite angles
RHOMBI
A Rhombus Is A Parallelogram With
4 Congruent Sides
All 5 Things About Parallelograms Are True…PLUS
4 congruent sides
Diagonal are perpendicular
Diagonals bisect opposite angles

16. 4 congruent sides 10
3Y + 1 = 10
3Y = 9
Y = 3
3Y + 1

17. Diagonal are perpendicularB 5
AB =
The perimeter Of
rhombus ABCD =
XC =
DB = 3 4 X 20 D C 3 8

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

19. QUADRILATERALS
PARALLELOGRAMS
RECTANGLES
RHOMBI
SQUARES

20. Theorem 1
If the diagonals of a parallelogram are perpendicular then it is a rhombus.
If one diagonal of a parallelogram bisects the pair of opposite angles then the parallelogram is a rhombus.
If the diagonals of a parallelogram are congruent then it is a rectangle.

21. Polygon Hierarchy Polygons Quadrilaterals Parallelograms Kites
Trapezoids
Isosceles Trapezoids
Rectangles
Rhombi
Squares

22. Quadrilateral Characteristics Summary
Convex Quadrilaterals
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Parallelograms
Trapezoids
Bases Parallel
Legs are not Parallel
Leg angles are supplementary
Median is parallel to bases Median = ½ (base + base)
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
Rectangles
Rhombi
Isosceles Trapezoids
All sides congruent
Diagonals perpendicular
Diagonals bisect opposite angles
Angles all 90°
Diagonals congruent
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Squares
Diagonals divide into 4 congruent triangles

23. Objectives Recognize and apply the properties of rhombi
All Parallelogram Properties
All 4 Sides Congruent
Diagonals bisect a pair of opposite ’s
Diagonals form right angles with each other
Recognize and apply the properties of squares
All Rectangle Properties
All Rhombus Properties
Diagonals divide into 4 congruent ∆’s ( )

24. Vocabulary Rhombus – quadrilateral with all four sides congruent
Square – a quadrilateral that is both a rhombus and a rectangle

25. Rhombi and Squares A
Rhombus Characteristics All Parallelogram Properties
All 4 Sides Congruent
Diagonals bisect a pair of opposite ’s
Diagonals form right angles with each other B C D A B
Square Characteristics All Parallelogram Properties All Rectangle Properties
All Rhombus Properties
Diagonals divide into 4 congruent ∆’s C D

26. Kayla has a garden whose length and width are each 25 feet
Kayla has a garden whose length and width are each 25 feet. If she places a fountain exactly in the center of the garden, how far is the center of the fountain from one of the corners of the garden?
Answer: about 17.7 feet
Example 5-4d

27. Textbook: page 348 Guided Practice: 1 thru 7 Practice/homework:
8 thru 13, 17 thru 22