Download 7-4 Classifying Polygons

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Page 341
7-4
Learn to classify and
find angles in polygons.
Vocabulary
polygon
regular polygon
trapezoid
parallelogram
rectangle
Classifying Polygons
Kites have been around for over
3000 years, when the Chinese
made them from bamboo and silk.
The most common flat kite is in
the shape of a diamond, a type of
quadrilateral called a kite.
A polygon is a closed plane
figure formed by three or more
segments. A polygon is named
by the number of its sides.
rhombus
Polygon
square
EXAMPLE
1
Number of Sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
n-gon
n
Quadrilateral
Pentagon
Hexagon
Finding Sums of the Angle Measures in Polygons
Find the sum of the angle measures in each figure.
Find the sum of the angle measures in a quadrilateral.
Divide the figure into triangles.
2 180° 360°
2 triangles
Find the sum of the angle measures in a pentagon.
Divide the figure into triangles.
3 180° 540°
3 triangles
Look for a pattern between the number of sides and the number of triangles.
Hexagon:
6 sides
4 triangles
Heptagon:
7 sides
5 triangles
7-4 Classifying Polygons
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The pattern is that the number of triangles is always 2 less than the
number of sides. So an n-gon can be divided into n 2 triangles. The
sum of the angle measures of any n-gon is 180°(n 2).
All the sides and angles of a regular polygon have equal measures.
EXAMPLE
2
Finding the Measure of Each Angle in a Regular Polygon
Find the angle measures in each regular polygon.
y°
x°
x°
x°
x°
x°
y°
y°
y°
y°
y°
5 congruent angles
5x° 180°(5 2)
5x° 180°(3)
5x° 540°
6 congruent angles
6y ° 180°(6 2)
6y ° 180°(4)
6y ° 720°
5x°
540°
5
5
6y°
720°
6
6
x° 108°
y ° 120°
Quadrilaterals with certain properties are given additional names. A
trapezoid has exactly 1 pair of parallel sides. A parallelogram has 2 pairs
of parallel sides. A rectangle has 4 right angles. A rhombus has 4
congruent sides. A square has 4 congruent sides and 4 right angles.
Quadrilaterals
Trapezoids
exactly 1 pair of
parallel sides
Parallelograms
2 pairs of parallel sides
Rectangles
4 right angles
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Chapter 7 Foundations of Geometry
Rhombuses
Squares
4
congruent
sides
4 congruent sides
4 right angles