Download Geo_Lesson 6_1

CHAPTER 6
Quadrilaterals
QUAD: Four
LATERAL: Related
to, situated at, or
on the side
Examples of Quadrilaterals
Kite
Lifting Platform
Suspension
Chapter Outline
• 6.1: Polygons
• 6.2: Parallelograms
• 6.3: Proving Quadrilaterals are Parallelograms
Quiz
• 6.4: Rhombuses, Rectangles, Squares
• 6.5: Trapezoids & Kites
Quiz
• 6.6: Special Quadrilaterals
• 6.7: Areas of Triangles & Quadrilaterals
Chapter 6 Exam
Geometry
Lesson 6.1
Polygons
• Use the prefixes in the table and the given
definition to define the new word
• Triplet: One of three children born at one birth
One of four children…
Quadruplet: _______________________________
• Decathlon: a 10-event athletic contest
A five-event athletic contest
– Pentathlon: _______________________________
• Hexapod: Having six legs or feet
Having three legs or feet
– Tripod: __________________________________
• Pentagram: A five-pointed star
A six-pointed star
– Hexagram: ________________________________
A plane figure that meets the
following three conditions:
1. Formed by three or more segments
called sides
2. No two sides with a common
endpoint are collinear
Yes
No
3. Each side intersects exactly two
other sides, one at each endpoint
Naming Polygons
• Vertex: The endpoint of a side
Q
Vertex
R
P
Side
S
T
• Naming a polygon: List the vertices
consecutively (in order)
– Polygon PQRST, QPTSR, etc.
Example 1
• Is the figure a polygon?
Yes!
No
(Some sides
intersect more
than two sides)
Yes!
No
(Has side that’s
not a segment)
Yes!
No
(Two sides intersect
only one side)
Name = Number of Sides
Number of Sides
3
4
5
6
7
8
9
10
12
N
Polygon Name
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
N-gon
• Convex: No line extending from a
side goes inside the polygon
Interior
Interior
• Concave: A line extending from a
side goes inside the polygon
Example 2
• Name the polygon by the number of
sides and tell if it is concave or convex
(a)
(b)
(c)
6 sides=hexagon 7 sides=heptagon
concave
convex
7 sides=heptagon
concave
Polygon Sides and Angles
Polygon
• All sides are congruent
Polygon
• Interior angles are congruent
Polygon
• Equilateral and equiangular
of Polygons
• A segment that joins two
nonconsecutive vertices
A
AC and BD are
B
diagonals of
polygon ABCD
D
C
Example 3
• Name the polygon by its
number of sides
7 sides = heptagon
• If ABCDEFG is one name,
what are two others?
BCDEFGA, EFGABCD, and many, many others
• Name all diagonals with
vertex E as an endpoint
EG, EA, EB, EC
• Name all non-consecutive
angles to A C, D, E, F
• The sum of the measures of the
interior angles of a quadrilateral is
360°
m1 + m2 + m3 + m4 = 360°
A
1
180°
D
4
2
B
180° 3
C
Why?
The diagonals divide it
into two triangles,
each having 180°
Example
• Find the sum of the interior angles of
the polygon
(a)
(b)
(c)
3 triangles
3(180°) = 540°
4 triangles
4(180°) = 720°
6 triangles
6(180°) = 1080°
Example 4
• Find x…
(5x+30)°+(10x-10)°+(8x-1)°+(6x-7)°=360°
(29x + 12)° = 360°
29x = 348
x = 12
(a)
Practice 5: Find x
(b)
(c)
Assignment
Ch 6.1 w/s