Download Is it a Polygon? - Hancock High School

==
Geometry Opener(s) 10/9
10/9
It’s World Post Day!!! Happy Birthday Scotty
McCreery, Brandon Routh, Sean Lennon, P.J.
Harvey, Guillermo del Toro, Scott Bakula, Tony
Shalhoub, Jackson Browne, John Lennon, Yusef
Lateef, Aimee Semple McPherson and Camille
Saint-Saens!!!
10/9
What to do today:
1. Do the opener.
2. Take notes.
3. Practice using polygon definitions.
4. Use whiteboards.
5. Practice identifying angle pairs.
6. Practice identifying polygon shapes.
7. Work on homework.
8. Do the exit pass.
TODAY’S OPENER
Agenda
1. Opener (5)
2. Period 1: Lecture/Notes: Definition Decisions
(15)
3. Practice: p. 48, #1-11 (Period 6: minus #5-6)
(12)
4. Whiteboard practice 1: Some figures to play
around with (??)
5. Whiteboard practice 2: Reading the Lesson
and Wksht. 1-6, p. 31 (15)
6. HW: Wksht. 1-6, p. 32 & 33 (Period 6: p. 32 in
class) (16…Period 1: 1 minute)
7. Exit Pass (5)
Essential Question(s)
 How do I describe polygons?
Objective(s)
 Students will be able to (SWBAT) identify
closed versus open polygons.
 SWBAT identify regular vs. irregular polygons.
 SWBAT identify simple vs. complex polygons.
 SWBAT identify concave vs. convex polygons.
 SWBAT find perimeters of polygons.
 SWBAT determine polygon side lengths based
on perimeter value and # of sides.
1. Two angles are complementary. The
measure of one angle is 21 more than twice
the measure of the other angle. Find the
measures of the angles.
Answer?
THE LAST OPENER
1. Imagine a big, giant coordinate plane on top of a
map of the U.S. A line segment starts at Chicago at
(1,-3) and ends at St. Louis at (-12, -13). What is
the distance between Chicago and St. Louis?
Answer?
Exit Pass
Connect D, E and F and C to create a polygon. Classify the polygon
in terms of the definitions we recorded yesterday and today.
The Last Exit Pass
⃗⃗⃗⃗⃗
QP and ⃗⃗⃗⃗⃗
QR are opposite rays, and ⃗⃗⃗⃗⃗
QT bisects RQS.
1. If mRQT = 6x + 5 and mSQT = 7x – 2,
find mRQT.
2. If mRQS = 22a – 11 and mRQT = 12a – 8,
find mTQS
S
T
R
P
Q
3.
HOMEWORK Period 1
Wksht. 1-6, p. 32.
Angle Vocabulary/Algebra quiz on Friday.
HOMEWORK Period 6
Same as Period 1.
Extra Credit
Period 1
Period 6
Stephanie M. (11x)
Magda (5x)
Prisma (2x)
Crystal (4x)
Bianca (4x)
Jonatan
Josie (8x)
Alejandra (2x)
Stephanie C.
Prisma
Ayelen (2x)
Saul (5x)
Michael
Yasmin
Sandra
Refugio
Ileanna (2x)
Demina
Melanie B. (5x)
Valerie (9x)
Denise (4x)
Isaias (2x)
Chris
Jocelyn
Lorenzo (2x)
Cynthia (2x)
Sergio (8x)
Lily (6x)
Jasmine
Yulissa
Edwin (2x)
Odalys
Carlos
Carolina (2x)
Melanie G.
NOTES: Rays, Angles & Protractors
Name
Definition
9/24
Figure
Notation
2. Angle ()
An initial point or endpoint with an
infinite number of points extending in
one direction.
2 rays that share the same endpoint.
3.  side
Each ray that makes up the angle.
Same as a Ray.
4. Degree
1/360th of a full circle.
23°
1. Ray
5. Degree measure How big/small the angle is in degrees.
6.  arc
7. Vertex of an 
8. Interior of an 
9. Exterior of an 
10.Right 
11.Acute 
12.Obtuse 
13.Reflex 
14.Straight 
15.Congruent 
16. Bisector
What’s
new?
The curved line inside an angle that
distinguishes its interior from its
exterior.
The endpoint of the two sides of an
angle.
The inside of an angle, denoted by the
arc. (yellow)
The outside of an angle, denoted by
the ABSENCE of an arc. (green)
An angle formed by 2 perpendicular
rays, its measure equal to 90°
An angle formed by 2 rays, its
measure less than 90°
An angle formed by 2 rays, its
measure greater than 90°
An angle formed by 2 rays, its
measure greater than 180°
An angle formed by 2 opposite rays,
its measure equal to 180°
2 angles that have the same degree
measure.
A ray with an endpoint that is
identical to the vertex of an angle
and which divides that angle in half
⃖⃗⃗⃗⃗
𝐼𝐹
BED
mABC = 36°
A curved line touching the
two rays of an angle.
A single uppercase printed
letter: the middle letter of a
named angle. (B in ABC)
mABC = 90°
mABC < 90°
180 > mABC > 90°
360 > mABC > 180°
mABC = 180°
ABC ≅ DEF
⃗⃗⃗⃗⃗
BG
NOTES: Angle Pairs
9/30
Special Pairs with Special Names
Adjacent angles.
Vertical angles.
Linear pair.
below,
Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the
lines connect up).
Polygon
(straight sides)
Not a Polygon
(has a curve)
Not a Polygon
(open, not closed)
Polygon comes from Greek. Poly- means "many" and -gon means "angle".
Types of Polygons
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
Regular
Irregular
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than
180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)
Convex
Concave
Simple or Complex
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects
itself! Many rules about polygons don't work when it is complex.
Simple Polygon
(this one's a Pentagon)
Complex Polygon
(also a Pentagon)
More Examples
Irregular Hexagon
Concave Octagon
Complex Polygon
(a "star polygon",
in this case a pentagram)
Names of Polygons
If it is a Regular Polygon...
Name
Sides
Shape
Interior Angle
Triangle (or Trigon)
3
60°
Quadrilateral (or Tetragon)
4
90°
Pentagon
5
108°
Hexagon
6
120°
Heptagon (or Septagon)
7
128.571°
Octagon
8
135°
Nonagon (or Enneagon)
9
140°
Decagon
10
144°
Hendecagon (or Undecagon)
11
147.273°
Dodecagon
12
150°
Triskaidecagon
13
152.308°
Tetrakaidecagon
14
154.286°
Pentadecagon
15
156°
Hexakaidecagon
16
157.5°
Heptadecagon
17
158.824°
Octakaidecagon
18
160°
Enneadecagon
19
161.053°
Icosagon
20
162°
Triacontagon
30
168°
Tetracontagon
40
171°
Pentacontagon
50
172.8°
Hexacontagon
60
174°
Heptacontagon
70
174.857°
Octacontagon
80
175.5°
Enneacontagon
90
176°
Hectagon
100
176.4°
Chiliagon
1,000
179.64°
Myriagon
10,000
179.964°
Megagon
1,000,000
~180°
Googolgon
10100
~180°
n-gon
n
(n-2) × 180° / n
You can make names using this method:
Sides
Start with...
Sides ...end with
20
Icosi...
+1
...henagon
30
Triaconta...
+2
...digon
40
Tetraconta...
+3
...trigon
50
Pentaconta...
+4
...tetragon
60
Hexaconta...
+5
...pentagon
70
Heptaconta...
+6
...hexagon
80
Octaconta...
+7
...heptagon
90
Enneaconta...
+8
...octagon
100
Hecta...
+9
...enneagon
etc..
Example: a 62-sided polygon is a Hexacontadigon
BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100gon", etc.
Some Figures to Angle Around With
Z
S
W
P
Y
V
T
R
Q
X
U
A
B
F
4
3
K
C
2
B
1
D
E
J
H
G