1.4 Polygons
Objectives: • Define and classify polygons
Aug 19­1:42 PM
DEFINITIONS
polygons
NOT polygons
Define: _________________________________
convex polygons
concave polygons
Aug 19­2:16 PM
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Definitions
A polygon is a closed figure in a plane that is formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. (The segments are commonly called sides, and the endpoint where they meet are vertices.)
A diagonal of a polygon is a line segment that connects any two non­consecutive vertices.
A concave polygon is a polygon where at least one diagonal lies outside the polygon.
A convex polygon is a polygon where no diagonals lie outside the polygon.
An equilateral polygon is a polygon where all the sides have equal length.
An equiangular polygon is a polygon where all the angles are congruent.
A regular polygon is a polygon that fits in with the other ones.
The last one was a joke.
A regular polygon is a polygon that is both equilateral and equiangular.
Aug 19­1:48 PM
iff stands for "if and only if"
The statement means that the hypothesis and conclusion of a conditional statement can be switched and be valid. Example:
If polygons are congruent, then corresponding sides and angles are congruent.
The converse statement:
If corresponding sides and angles are congruent, then polygons are congruent.
OR, to say both:
Polygons are congruent iff the corresponding sides and angles are congruent.
Aug 19­2:21 PM
2
SIDES
NAME
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
8
octagon
9
nonagon
10
decagon
11
undecagon
12
dodecagon
n
n­gon
Polly
Aug 19­2:19 PM
In naming congruent polygons, make sure the letters correspond!
D
C
A
T
G
O
ΔCAT ≅ Δ___
Aug 19­2:33 PM
3
Assignment: due next class 1.4 p56 1­6,9­15,17­21,25,28,30
Aug 19­3:17 PM
Sep 7­2:50 PM
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