Exploring Polygons
What are polygons?
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
The following are examples of polygons:
The figures below are not polygons. Can you tell why?
Regular Polygons
A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.
The following are examples of regular polygons:
Would a square be a regular polygon? A rectangle?
The following are not examples of regular polygons:
How do you know?
TrianglesAll three-sided polygons.
There are many special types of triangles.
QuadrilateralA four-sided polygon.
Angles in quadrilaterals…Quadrilaterals have four sides and four angles.
The sum of the measures of the angles is 360°.
Find the value of x in the quadrilateral below
x° + 105° + 80° + 95° = 360°
Add 105°, 80°, and 95°.
x° + 280° = 360°
THINK: What measure
added to 280° equals 360°?
80° + 280° = 360°
x° = 80°
Find the value of x in each quadrilateral.
A rectangle has opposite sides congruent and parallel, and all right
angles.
Are rectangles a kind of quadrilateral?
How do you know?
A square has all sides congruent, opposite sides parallel, and all right
angles.
Are squares a kind of rectangle?
How do you know?
A parallelogram has opposite sides congruent and parallel, and opposite
angles congruent.
Are parallelograms a kind of rectangle? How do you know?
A rhombus has all sides congruent, opposite sides parallel, and opposite
angles congruent.
How are rhombuses and squares similar? How are rhombuses and squares different?
A trapezoid has exactly one pair of opposite sides parallel.
There are special types of trapezoids ….that’s for another day!
Classify each quadrilateral.
PentagonA five-sided polygon
a regular pentagon
an irregular pentagon
HexagonA six-sided polygon.
a regular hexagon
an irregular hexagon
HeptagonA seven-sided polygon
A regular heptagon
an irregular heptagon
OctagonAn eight-sided polygon.
A regular octagon
An irregular octagon
NonagonA nine-sided polygon.
A regular nonagon
An irregular nonagon
DecagonA ten-sided polygon.
A regular decagon
An irregular decagon