1. Have out: U9D8 Bellwork: Pencil, highlighter, GP NB, red pen, textbook
Solve for x in the figures below. Be sure to justify your answers!
regular octagon x
197° 2x
3x – 7
129°
x + 5
2x + 24 +1 +1
m of ONE interior of regular n-gon
Sum of interior s of n-gon = 180(n – 2)
x x+3x–7+2x+129+x+5=180(7– 2)
(n = 8) +1 +1 +1
9x = 180(5)
9x = 900
9x = 576 +1
x = 64° +1
x = 55.5°

2. Recall that Venn diagrams show all of the possible relationships between groups of things.
Let’s create a Venn diagram illustrating the age at which people legally earn the following privileges and rights in the U.S.:
Drive
Smoke
Gamble and Drink in Las Vegas

3. Venn Diagram of Sins Drive Smoke 18 Ages: 16 19 20 5 19 17 12 20 21 2298 18 98 5 12
Gamble and Drink

4. Add to your resource page... Quadrilaterals
Here is an organizer to help understand the relationships between the quadrilaterals.
Add to your
resource page...
Quadrilaterals
Trapezoids
Polygons
Polygons
Isosceles Trapezoid
Parallelograms
Rectangles
Rhombus
Squares
Kites

5. Here’s another way of looking at the classification of quadrilaterals.
Add to your
resource page...
Quadrilaterals
Parallelogram
>>
>
Trapezoid
>>
Kite
Rhombus
Rectangle
Isosceles Trapezoid
>>
Square

6. Add to Quadrilateral Toolkit: If it’s a rectangle  the diagonals .
US – 91
Draw in the diagonals in the rectangle.
a) What do you notice about the lengths of the diagonals? Write a conjecture.
If it is a rectangle, then the diagonals are congruent. P S
b) Prove your conjecture.
Statement
Reason
1. PQRS is a _________
rectangle
1. ________________
Given
2. mQPS = ______=____
mRSP
90°
2. Definition of _________
rectangle
3. __________
3. ________________
If parallelogram  opposite sides 
4. __________
4. ________________
Reflexive property
5. ∆QPS _____
RSP
5. ________________
SAS
6. ________________
6. ________________
 s   parts
Add to Quadrilateral Toolkit: If it’s a rectangle  the diagonals .

7. Add to Quadrilateral Toolkit: If it’s a rhombus  the diagonals are .
Figure DOVE is a rhombus. Use the fact that a rhombus is a special kind of parallelogram to prove the following: D O R
a) The diagonals of a rhombus are perpendicular. E V
Statement
Reason
1. DOVE is a _________
rhombus
1. ____________________
Given
2. ____________________
2. Definition of _________
rhombus
3. __________ & __________
3. ____________________
If parallelogram  diagonals bisect each other (US – 81)
4. ∆DOR _______________
VOR VER DER
4. ____________________
SSS
5. ______________
DRO VRO
5. ____________________
 s   parts
6. mDRO + mVRO = ______
180°
6. ____________________
Linear pair
7. mDRO = mVRO = ______
90°
7. Substitution & division
8. ____________________
8. ____________________
Definition of perpendicular
Add to Quadrilateral Toolkit: If it’s a rhombus  the diagonals are .

8. US – 92
Figure DOVE is a rhombus. Use the fact that a rhombus is a special kind of parallelogram to prove the following: D O R
b) The diagonals of a rhombus bisect the angles of the rhombus. E V
Statement
Reason
1. ∆DOR _______________
VOR VER DER
1. ____________________
SEE ABOVE!!!
2. _____________, _____________,
_____________, _____________
RDO RDE
RVO RVE
2. ____________________
 s   parts
ROD ROV
REV RED
3. ______ bisects EDO and EVO
3. ____________________
Definition of bisect
______ bisects DOV and DEV
Add to Quadrilateral Toolkit: If it’s a rhombus  the diagonals bisect the angles of the rhombus.

9. US – 93
The length of each side of a rhombus is 10 cm and mA = 60°. Find the length of the longer diagonal, AC. You will need to use the properties of a rhombus to get all the data you need.
(rhombus diagonals bisect the s.) B
10 cm C
10 cm
10 cm
30°
60°
mBAC = 30° A D
10 cm
(rhombus  the diagonals are .)
ACBD
30°-60°-90° 
(Parallelogram diagonals bisect each other)
SL: n =
LL:
Hyp: 2n =
5cm
10cm

10. b) Find the lengths of each of the sides of MATH.
US – 94
a) Graph each of the following equations on the same set of axes. Darken in the region bounded by all four lines. y
b) Find the lengths of each of the sides of MATH.
(Pythagorean Thm.)
(Pythagorean Thm.)
MA = 5 units T
TH = 5 units
AT = 5 units
MH = 5 units A
c) What type of quadrilateral is MATH? Why? H
MATH is a rhombus by definition because all four sides are congruent. M x
d) Draw the diagonals of MATH and write the equation for each diagonal.

11. Work on US
& worksheet.

12. How it works... Kingdom Phylum Class Order Family Genus Species
Think about the scientific classifications of animals you learned in biology:
How it works...
Kingdom
Kingdom Phylum Class Order Family Genus Species
Phylum
Most general
Class
Order
Family
Genus
Species
Most specific

13. How it works... For example, humans are classified as such: Animalia
Where would you place the following?
Chordata
Mammalia
Primates
Hominidae
Homo
Sapien