1. Let’s review the quadrilateral properties we’ve learned so far:
All Quadrilaterals
Four angles
Four sides
Angles add to °360
Parallelograms
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other

2. Today we’re going to learn about special parallelograms
Quadrilaterals – Day 3
Rectangle
Today we’re going to learn about special parallelograms
Rhombus
Square

3. All Quadrilaterals
Parallelogram
Rectangle

4. Rectangle Is a parallelogram
Has all the properties of quadrilaterals above it in the flow chart
PLUS has the following special properties:
Angles are 90°
Diagonals are congruent (contractor’s theorem)

5. All Quadrilaterals
Rhombi
Parallelograms
Rectangles

6. Rhombus PLUS has the following special properties: Is a parallelogram
Has all the properties of quadrilaterals above it
PLUS has the following special properties:
Sides are congruent
Diagonals are perpendicular
Diagonals are angle bisectors

7. Square is the love child of the rectangle and rhombus
All Quadrilaterals
Rhombus
Parallelogram
Rectangle
Square
SQUARE
Square is the love child of the rectangle and rhombus

8. Has all the properties of quadrilaterals above it in the flow chart.
SQUARE
Dad = Rectangle Mom = Rhombus
It gets the congruent sides mom
It gets the angles from dad
It gets the congruent diagonals from dad
It gets perpendicular diagonals from mom
It gets angle bisector diagonals from mom

9. Euler (pronounced ‘oiler’)
All Quadrilaterals
Rhombus
Parallelogram
Rectangle
Square
Venn
Diagram
Euler (pronounced ‘oiler’)
Diagram

10. I never realized there was so much to learn about quadrilaterals!
Whew….
I never realized there was so much to learn about quadrilaterals!

11. F M D E R 14 in. 20° 26 in. Let’s practice…
Find the measures of all the sides, diagonals and angles.
Let’s practice…
FRED is a rectangle F M D E R
14 in.
26 in.
20°
mDM = 15 in.

12. CRIS is a rhombus Find all angle, side and diagonal measures
28°
8 ft
17 ft
15 ft C S

13. True or False
Every square is a rhombus
Every rhombus is a square
Every rectangle is a square
Every square is a rectangle
All rhombi are parallelograms
Every parallelogram is a rectangle.

14. Quadrilaterals Day 4
Kite Trapezoid Trapezium

15. Convex Quadrilaterals Parallelograms Rectangles Rhombi Square
Trapezoid
Right Trapezoid
Isosceles Trapezoid
Trapezium
Kite
This is what the flow chart will look like at the end of this class.

16. Properties of a trapezoid
A trapezoid has one and only one pair of parallel sides.
Two pair of consecutive, supplementary angles.

17. Midsegment of a trapezoid
As the name suggests, a midsegment of a trapezoid is a segment in the middle of a trapezoid.
It is parallel with the parallel sides.
Behold

18. Properties of a trapezoid
Which is the midsegment?
Which is not?

19. Properties of a trapezoid
The length of the midsegment is the average of the lengths of the parallel sides.
The midsegment is equidistant from each parallel side.
Length 1
Length 1 + Length 2 2
Length 2

20. Properties of a trapezoid
Let’s practice 10 x
= 15 16
2x - 4 20 24
2x + 4
CHECK
2x x + 2 = 2x + 4 2
Does = 24? 2
3x + 2 32
5x - 2 = 2x + 4 2
If yes, have a personal celebration!!
5x - 2 = 4x + 8
If no, then find your mistake or start over.
X = 10

21. Try this
Find the lengths of the parallel segments when x = 2 A B C Z Y M X
X + 5 ?
AM = 2
BY = 7
CZ = 12
Check to make sure these numbers work…
Find ?
= 7 2
? = X + 10
YEA!!

22. Try this…
If AZ = 31 and
CX = 25, find BY
BY = 28 C X Y B A Z

23. Properties of a TRAPEZIUM: A quadrilateral with NO parallel sides.
A special Trapezium is a KITE
2 pair of consecutive congruent sides
Opposite sides are NOT congruent
Only ONE pair of opposite angles are congruent.
Diagonals are perpendicular
Only ONE diagonal
is bisected

25. White boards…

26. Your Assignment
6-6 Worksheet