Transcript Lesson 1 Contents

Lesson 1-6
Polygons
5-Minute Check on Lesson 1-5
Transparency 1-6
A
Refer to the figure for questions 1 through 3.
1. Name two acute vertical angles.
D
48°
E
2. Name a linear pair whose vertex is E.
B
C
3. Name an angle supplementary to BEC.
4. If 1 and 2 are supplementary and the measure of 1 is twice that of 2,
then find the measures of both angles.
5. If RS  ST and SV is the angle bisector of RST, what is the m TSV?
6.
Standardized Test Practice:
If two angles are congruent and supplementary,
then they must be
A
two right angles
B
two acute angles
C
two obtuse angles
D
an acute and an obtuse angle
Click the mouse button or press the
Space Bar to display the answers.
5-Minute Check on Lesson 1-5
Transparency 1-6
A
Refer to the figure for questions 1 through 3.
1. Name two acute vertical angles.
D
48°
m AEB = m DEC = 48°
E
2. Name a linear pair whose vertex is E.
Samples: AEB and AED or BEC and CED
B
C
3. Name an angle supplementary to BEC.
Either AEB or DEC
4. If 1 and 2 are supplementary and the measure of 1 is twice that of 2,
then find the measures of both angles. m1 + m2 = 180 supplementary
m1 = 2m2
so 2m2 + m2 = 180
3m2 = 180
m2 = 60°
m1 = 120°
5. If RS  ST and SV is the angle bisector of RST, what is the m TSV?
m TSV = ½ m RST = ½(90) = 45°
6.
Standardized Test Practice:
If two angles are congruent and supplementary,
then they must be
A
two right angles
B
two acute angles
C
two obtuse angles
D
an acute and an obtuse angle
Click the mouse button or press the
Space Bar to display the answers.
Objectives
• Identify and name polygons
• Find perimeters of polygons
Vocabulary
• Polygon – a closed figure whose sides are all
line segments
• n-gon – a polygon with n sides
• Concave – any line aligned to the sides
passes through the interior
• Convex – not concave (“side line” passes
through interior)
• Regular polygon – a convex polygon with all
segments congruent & all angles congruent
• Irregular polygon – not regular
• Perimeter – the sum of the lengths of sides
of the polygon
Not a Polygon
Figure is not closed
Sides are not
line segments
Polygons
Side
extended
goes
through
interior
Concave
Convex
Not Concave
All extended sides
stay outside interior
Interior Angle
> 180°
All Interior Angles
less than 180°
Irregular
Not Regular
Regular
All Sides same
All Angles same
Perimeter
P=a+b+c+d+e+f
e
f
d
Once around
the figure
a
c
b
If regular,
then a = b = c = d = e = f
and P = 6a
Names of Polygons
Number
of Sides
Name
Sum of
Interior
Angles
3
4
Triangle
Quadrilateral
180
360
5
6
7
Pentagon
Hexagon
Heptagon
540
720
900
8
9
Octagon
Nonagon
1080
1260
10
12
n
Decagon
Dodecagon
N-gon
1440
1800
(n-2) • 180
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass through the
interior of the quadrilateral, so it is convex.
The sides are not congruent, so it is irregular.
Answer: quadrilateral, convex, irregular
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or irregular.
There are 9 sides, so this is a nonagon.
A line containing some of the sides will pass through the
interior of the nonagon, so it is concave.
The sides are not congruent, so it is irregular.
Answer: nonagon, concave, irregular
CONSTRUCTION
A masonry company is contracted to lay three
layers of decorative brick along the foundation for a
new house given the dimensions below. Find the
perimeter of the foundation.
Add the side’s lengths
The width of a rectangle is 5 less than twice its length.
The perimeter is 80 centimeters.
Find the length of each side.
Let
represent the length. Then the width is
P=l
+ w + l + w = 2(l + w)
.
Perimeter formula for rectangle
Multiply.
Simplify.
Add 10 to each side.
Divide each side by 6.
The length is 15 cm. By substituting 15 for ,
the width becomes 2(15) – 5 or 25 cm.
Answer:
Summary & Homework
• Summary:
– A polygon is a closed figure made of line
segments
– The perimeter of a polygon is the sum of the
lengths of its sides
• Homework:
– pg 49-50: 12-21, 29-31, 33